diff --git a/src/browser/Terminal2.test.ts b/src/browser/Terminal2.test.ts
index 44540c6e2..4965e8f36 100644
--- a/src/browser/Terminal2.test.ts
+++ b/src/browser/Terminal2.test.ts
@@ -17,6 +17,7 @@ const ROWS = 25;
 
 const TESTFILES = glob.sync('**/escape_sequence_files/*.in', { cwd: path.join(__dirname, '../..')});
 const SKIP_FILES = [
+  't0055-EL.in',            // EL/ED handle cursor at cols differently (see #3362)
   't0084-CBT.in',
   't0101-NLM.in',
   't0103-reverse_wrap.in',  // not comparable, we deviate from xterm reverse wrap on purpose
diff --git a/src/common/InputHandler.test.ts b/src/common/InputHandler.test.ts
index 676b1e453..902640f90 100644
--- a/src/common/InputHandler.test.ts
+++ b/src/common/InputHandler.test.ts
@@ -1913,6 +1913,92 @@ describe('InputHandler', () => {
       });
     });
   });
+
+  // issue #3362 and #2979
+  describe('EL/ED cursor at buffer.cols', () => {
+    beforeEach(() => {
+      bufferService.resize(10, 5);
+    });
+    describe('cursor should stay at cols / does not overflow', () => {
+      it('EL0', async () => {
+        await inputHandler.parseP('##########\x1b[0K');
+        assert.equal(bufferService.buffer.x, 10);
+        assert.deepEqual(getLines(bufferService), ['#'.repeat(10), '', '', '', '']);
+      });
+      it('EL1', async () => {
+        await inputHandler.parseP('##########\x1b[1K');
+        assert.equal(bufferService.buffer.x, 10);
+        assert.deepEqual(getLines(bufferService), ['', '', '', '', '']);
+      });
+      it('EL2', async () => {
+        await inputHandler.parseP('##########\x1b[2K');
+        assert.equal(bufferService.buffer.x, 10);
+        assert.deepEqual(getLines(bufferService), ['', '', '', '', '']);
+      });
+      it('ED0', async () => {
+        await inputHandler.parseP('##########\x1b[0J');
+        assert.equal(bufferService.buffer.x, 10);
+        assert.deepEqual(getLines(bufferService), ['#'.repeat(10), '', '', '', '']);
+      });
+      it('ED1', async () => {
+        await inputHandler.parseP('##########\x1b[1J');
+        assert.equal(bufferService.buffer.x, 10);
+        assert.deepEqual(getLines(bufferService), ['', '', '', '', '']);
+      });
+      it('ED2', async () => {
+        await inputHandler.parseP('##########\x1b[2J');
+        assert.equal(bufferService.buffer.x, 10);
+        assert.deepEqual(getLines(bufferService), ['', '', '', '', '']);
+      });
+      it('ED3', async () => {
+        await inputHandler.parseP('##########\x1b[3J');
+        assert.equal(bufferService.buffer.x, 10);
+        assert.deepEqual(getLines(bufferService), ['#'.repeat(10), '', '', '', '']);
+      });
+    });
+    describe('following sequence keeps working', () => {
+      // sequences to test (cursor related ones)
+      const SEQ = [
+        /* ICH */   '\x1b[10@',
+        /* SL */    '\x1b[10 @',
+        /* CUU */   '\x1b[10A',
+        /* SR */    '\x1b[10 A',
+        /* CUD */   '\x1b[10B',
+        /* CUF */   '\x1b[10C',
+        /* CUB */   '\x1b[10D',
+        /* CNL */   '\x1b[10E',
+        /* CPL */   '\x1b[10F',
+        /* CHA */   '\x1b[10G',
+        /* CUP */   '\x1b[10;10H',
+        /* CHT */   '\x1b[10I',
+        /* IL */    '\x1b[10L',
+        /* DL */    '\x1b[10M',
+        /* DCH */   '\x1b[10P',
+        /* SU */    '\x1b[10S',
+        /* SD */    '\x1b[10T',
+        /* ECH */   '\x1b[10X',
+        /* CBT */   '\x1b[10Z',
+        /* HPA */   '\x1b[10`',
+        /* HPR */   '\x1b[10a',
+        /* REP */   '\x1b[10b',
+        /* VPA */   '\x1b[10d',
+        /* VPR */   '\x1b[10e',
+        /* HVP */   '\x1b[10;10f',
+        /* TBC */   '\x1b[0g',
+        /* SCOSC */ '\x1b[s',
+        /* DECIC */ '\x1b[10\'}',
+        /* DECDC */ '\x1b[10\'~'
+      ];
+      it('cursor never advances beyond cols', async () => {
+        for (const seq of SEQ) {
+          await inputHandler.parseP('##########\x1b[2J' + seq);
+          assert.equal(bufferService.buffer.x <= bufferService.cols, true);
+          inputHandler.reset();
+          bufferService.reset();
+        }
+      });
+    });
+  });
 });
 
 
diff --git a/src/common/InputHandler.ts b/src/common/InputHandler.ts
index a2b5a7829..d3b29a702 100644
--- a/src/common/InputHandler.ts
+++ b/src/common/InputHandler.ts
@@ -1247,7 +1247,7 @@ export class InputHandler extends Disposable implements IInputHandler {
    * @vt: #P[Protection attributes are not supported.] CSI DECSED   "Selective Erase In Display"  "CSI ? Ps J"  "Currently the same as ED."
    */
   public eraseInDisplay(params: IParams): boolean {
-    this._restrictCursor();
+    this._restrictCursor(this._bufferService.cols);
     let j;
     switch (params.params[0]) {
       case 0:
@@ -1319,7 +1319,7 @@ export class InputHandler extends Disposable implements IInputHandler {
    * @vt: #P[Protection attributes are not supported.] CSI DECSEL   "Selective Erase In Line"  "CSI ? Ps K"  "Currently the same as EL."
    */
   public eraseInLine(params: IParams): boolean {
-    this._restrictCursor();
+    this._restrictCursor(this._bufferService.cols);
     switch (params.params[0]) {
       case 0:
         this._eraseInBufferLine(this._bufferService.buffer.y, this._bufferService.buffer.x, this._bufferService.cols);