diff --git a/src/Buffer.ts b/src/Buffer.ts
index 4f81025fe5..4c73006391 100644
--- a/src/Buffer.ts
+++ b/src/Buffer.ts
@@ -82,10 +82,10 @@ export class Buffer implements IBuffer {
     this.ybase = 0;
     this.y = 0;
     this.x = 0;
-    this.tabs = {};
     this._lines = new CircularList<LineData>(this._getCorrectBufferLength(this._terminal.rows));
     this.scrollTop = 0;
     this.scrollBottom = this._terminal.rows - 1;
+    this.setupTabStops();
   }
 
   /**
@@ -233,4 +233,47 @@ export class Buffer implements IBuffer {
 
     return lineString.substring(widthAdjustedStartCol, finalEndCol);
   }
+
+  /**
+   * Setup the tab stops.
+   * @param i The index to start setting up tab stops from.
+   */
+  public setupTabStops(i?: number): void {
+    if (i != null) {
+      if (!this.tabs[i]) {
+        i = this.prevStop(i);
+      }
+    } else {
+      this.tabs = {};
+      i = 0;
+    }
+
+    for (; i < this._terminal.cols; i += this._terminal.options.tabStopWidth) {
+      this.tabs[i] = true;
+    }
+  }
+
+  /**
+   * Move the cursor to the previous tab stop from the given position (default is current).
+   * @param x The position to move the cursor to the previous tab stop.
+   */
+  public prevStop(x?: number): number {
+    if (x == null) {
+      x = this.x;
+    }
+    while (!this.tabs[--x] && x > 0);
+    return x >= this._terminal.cols ? this._terminal.cols - 1 : x < 0 ? 0 : x;
+  }
+
+  /**
+   * Move the cursor one tab stop forward from the given position (default is current).
+   * @param x The position to move the cursor one tab stop forward.
+   */
+  public nextStop(x?: number): number {
+    if (x == null) {
+      x = this.x;
+    }
+    while (!this.tabs[++x] && x < this._terminal.cols);
+    return x >= this._terminal.cols ? this._terminal.cols - 1 : x < 0 ? 0 : x;
+  }
 }
diff --git a/src/BufferSet.ts b/src/BufferSet.ts
index d37a650f94..64b364e92f 100644
--- a/src/BufferSet.ts
+++ b/src/BufferSet.ts
@@ -28,6 +28,8 @@ export class BufferSet extends EventEmitter implements IBufferSet {
     // See http://invisible-island.net/xterm/ctlseqs/ctlseqs.html#h2-The-Alternate-Screen-Buffer
     this._alt = new Buffer(this._terminal, false);
     this._activeBuffer = this._normal;
+
+    this.setupTabStops();
   }
 
   /**
@@ -87,4 +89,13 @@ export class BufferSet extends EventEmitter implements IBufferSet {
     this._normal.resize(newCols, newRows);
     this._alt.resize(newCols, newRows);
   }
+
+  /**
+   * Setup the tab stops.
+   * @param i The index to start setting up tab stops from.
+   */
+  public setupTabStops(i?: number): void {
+    this._normal.setupTabStops(i);
+    this._alt.setupTabStops(i);
+  }
 }
diff --git a/src/InputHandler.ts b/src/InputHandler.ts
index f2d9775113..abfdfa0e6b 100644
--- a/src/InputHandler.ts
+++ b/src/InputHandler.ts
@@ -157,7 +157,7 @@ export class InputHandler implements IInputHandler {
    * Horizontal Tab (HT) (Ctrl-I).
    */
   public tab(): void {
-    this._terminal.buffer.x = this._terminal.nextStop();
+    this._terminal.buffer.x = this._terminal.buffer.nextStop();
   }
 
   /**
@@ -349,7 +349,7 @@ export class InputHandler implements IInputHandler {
   public cursorForwardTab(params: number[]): void {
     let param = params[0] || 1;
     while (param--) {
-      this._terminal.buffer.x = this._terminal.nextStop();
+      this._terminal.buffer.x = this._terminal.buffer.nextStop();
     }
   }
 
@@ -548,7 +548,7 @@ export class InputHandler implements IInputHandler {
   public cursorBackwardTab(params: number[]): void {
     let param = params[0] || 1;
     while (param--) {
-      this._terminal.buffer.x = this._terminal.prevStop();
+      this._terminal.buffer.x = this._terminal.buffer.prevStop();
     }
   }
 
diff --git a/src/Interfaces.ts b/src/Interfaces.ts
index 943003aec3..fb66f4d7cf 100644
--- a/src/Interfaces.ts
+++ b/src/Interfaces.ts
@@ -92,14 +92,12 @@ export interface IInputHandlingTerminal extends IEventEmitter {
   convertEol: boolean;
   updateRange(y: number): void;
   scroll(isWrapped?: boolean): void;
-  nextStop(x?: number): number;
   setgLevel(g: number): void;
   eraseAttr(): number;
   eraseRight(x: number, y: number): void;
   eraseLine(y: number): void;
   eraseLeft(x: number, y: number): void;
   blankLine(cur?: boolean, isWrapped?: boolean): LineData;
-  prevStop(x?: number): number;
   is(term: string): boolean;
   send(data: string): void;
   setgCharset(g: number, charset: Charset): void;
@@ -146,6 +144,8 @@ export interface IBuffer {
   savedY: number;
   savedX: number;
   translateBufferLineToString(lineIndex: number, trimRight: boolean, startCol?: number, endCol?: number): string;
+  nextStop(x?: number): number;
+  prevStop(x?: number): number;
 }
 
 export interface IBufferSet {
diff --git a/src/Terminal.ts b/src/Terminal.ts
index ea3800d0c5..827273ff52 100644
--- a/src/Terminal.ts
+++ b/src/Terminal.ts
@@ -392,8 +392,6 @@ export class Terminal extends EventEmitter implements ITerminal, IInputHandlingT
     if (this.selectionManager) {
       this.selectionManager.setBuffer(this.buffer);
     }
-
-    this.setupStops();
   }
 
   /**
@@ -486,7 +484,7 @@ export class Terminal extends EventEmitter implements ITerminal, IInputHandlingT
         this.buffers.resize(this.cols, this.rows);
         this.viewport.syncScrollArea();
         break;
-      case 'tabStopWidth': this.setupStops(); break;
+      case 'tabStopWidth': this.buffers.setupTabStops(); break;
       case 'bellSound':
       case 'bellStyle': this.syncBellSound(); break;
     }
@@ -1938,7 +1936,7 @@ export class Terminal extends EventEmitter implements ITerminal, IInputHandlingT
 
     this.cols = x;
     this.rows = y;
-    this.setupStops(this.cols);
+    this.buffers.setupTabStops(this.cols);
 
     this.charMeasure.measure();
 
@@ -1971,45 +1969,6 @@ export class Terminal extends EventEmitter implements ITerminal, IInputHandlingT
     this.refreshEnd = this.rows - 1;
   }
 
-  /**
-   * Setup the tab stops.
-   * @param {number} i
-   */
-  public setupStops(i?: number): void {
-    if (i != null) {
-      if (!this.buffer.tabs[i]) {
-        i = this.prevStop(i);
-      }
-    } else {
-      this.buffer.tabs = {};
-      i = 0;
-    }
-
-    for (; i < this.cols; i += this.getOption('tabStopWidth')) {
-      this.buffer.tabs[i] = true;
-    }
-  }
-
-  /**
-   * Move the cursor to the previous tab stop from the given position (default is current).
-   * @param {number} x The position to move the cursor to the previous tab stop.
-   */
-  public prevStop(x?: number): number {
-    if (x == null) x = this.buffer.x;
-    while (!this.buffer.tabs[--x] && x > 0);
-    return x >= this.cols ? this.cols - 1 : x < 0 ? 0 : x;
-  }
-
-  /**
-   * Move the cursor one tab stop forward from the given position (default is current).
-   * @param {number} x The position to move the cursor one tab stop forward.
-   */
-  public nextStop(x?: number): number {
-    if (x == null) x = this.buffer.x;
-    while (!this.buffer.tabs[++x] && x < this.cols);
-    return x >= this.cols ? this.cols - 1 : x < 0 ? 0 : x;
-  }
-
   /**
    * Erase in the identified line everything from "x" to the end of the line (right).
    * @param {number} x The column from which to start erasing to the end of the line.
diff --git a/src/utils/TestUtils.test.ts b/src/utils/TestUtils.test.ts
index 8d47556093..ae83aed4fb 100644
--- a/src/utils/TestUtils.test.ts
+++ b/src/utils/TestUtils.test.ts
@@ -189,6 +189,12 @@ export class MockBuffer implements IBuffer {
   translateBufferLineToString(lineIndex: number, trimRight: boolean, startCol?: number, endCol?: number): string {
     throw new Error('Method not implemented.');
   }
+  nextStop(x?: number): number {
+    throw new Error('Method not implemented.');
+  }
+  prevStop(x?: number): number {
+    throw new Error('Method not implemented.');
+  }
 }
 
 export class MockViewport implements IViewport {