diff --git a/lib/StreamingStore.ts b/lib/StreamingStore.ts
index 779fefb..d6a2ae8 100644
--- a/lib/StreamingStore.ts
+++ b/lib/StreamingStore.ts
@@ -40,14 +40,65 @@ implements RDF.Source<Q>, RDF.Sink<RDF.Stream<Q>, EventEmitter> {
     }
   }
 
-  protected importToListeners(stream: RDF.Stream<Q>): void {
-    stream.on('data', (quad: Q) => {
-      for (const pendingStream of this.pendingStreams.getPendingStreamsForQuad(quad)) {
-        if (!this.ended) {
-          pendingStream.push(quad);
-          pendingStream.emit('quad', quad);
-        }
+  /**
+   * This function will read the quad stream in an on-demand fashion, and will check if the quads already exist in the
+   * store. If they don't, they will be pushed into the storeImportStream, and the matching pendingStreams.
+   * @param stream A quad stream.
+   * @param storeImportStream A stream to import the quads into the store.
+   */
+  protected importToListeners(stream: RDF.Stream<Q>, storeImportStream: PassThrough): void {
+    let streamEnded = false;
+    stream.once('readable', async() => {
+      let quad: Q | null = stream.read();
+      while (quad) {
+        const staticQuad = quad;
+        await new Promise<void>(resolve => {
+          // Match the new quad with the store.
+          const matchStream = this.store.match(
+            staticQuad.subject,
+            staticQuad.predicate,
+            staticQuad.object,
+            staticQuad.graph,
+          );
+
+          // If the StreamingStore hasn't ended, we add the quad to the storeImportStream and the corresponding
+          // pendingStreams and resolve to handle the next quad.
+          const handleEnd = (): void => {
+            if (!this.ended) {
+              storeImportStream.push(staticQuad);
+              for (const pendingStream of this.pendingStreams.getPendingStreamsForQuad(staticQuad)) {
+                pendingStream.push(staticQuad);
+                pendingStream.emit('quad', staticQuad);
+              }
+            }
+            resolve();
+          };
+
+          // If the matchStream has a result, the quad already exists.
+          // We remove the 'end' listener and continue to the next quad.
+          matchStream.once('data', () => {
+            matchStream.removeListener('end', handleEnd);
+            resolve();
+          });
+
+          // If the matchStream has ended (and this listener isn't removed), the quad doesn't exist yet.
+          // So we call the handleEnd function.
+          matchStream.once('end', handleEnd);
+        });
+
+        quad = stream.read();
       }
+      // If the stream has ended, all quads will be read from the quad stream, so we can end the storeImportStream.
+      if (streamEnded) {
+        storeImportStream.end();
+        return;
+      }
+      // If the stream hasn't ended, we recursively call this function to wait for the stream to become readable again.
+      this.importToListeners(stream, storeImportStream);
+    });
+
+    stream.on('end', () => {
+      streamEnded = true;
     });
   }
 
@@ -56,8 +107,12 @@ implements RDF.Source<Q>, RDF.Sink<RDF.Stream<Q>, EventEmitter> {
       throw new Error('Attempted to import into an ended StreamingStore');
     }
 
-    this.importToListeners(stream);
-    return this.store.import(stream);
+    const storeImportStream = new PassThrough({ objectMode: true });
+    stream.on('error', error => storeImportStream.emit('error', error));
+
+    this.importToListeners(stream, storeImportStream);
+
+    return this.store.import(storeImportStream);
   }
 
   public match(
diff --git a/test/StreamingStore-test.ts b/test/StreamingStore-test.ts
index a10b7bc..87c359a 100644
--- a/test/StreamingStore-test.ts
+++ b/test/StreamingStore-test.ts
@@ -3,7 +3,7 @@ import arrayifyStream from 'arrayify-stream';
 import { promisifyEventEmitter } from 'event-emitter-promisify/dist';
 import { Store } from 'n3';
 import { DataFactory } from 'rdf-data-factory';
-import { Readable } from 'readable-stream';
+import { PassThrough, Readable } from 'readable-stream';
 import { StreamingStore } from '../lib/StreamingStore';
 const quad = require('rdf-quad');
 const streamifyArray = require('streamify-array');
@@ -465,4 +465,55 @@ describe('StreamingStore', () => {
         quad('s4', 'p4', 'o', 'g'),
       ]);
   });
+
+  it('handles duplicates in import (set-semantics)', async() => {
+    const match = store.match();
+    await promisifyEventEmitter(store.import(streamifyArray([
+      quad('s1', 'p1', 'o1'),
+      quad('s1', 'p1', 'o1'),
+    ])));
+    store.end();
+
+    expect(await arrayifyStream(match)).toEqualRdfQuadArray(
+      [ quad('s1', 'p1', 'o1') ],
+    );
+  });
+
+  it('handles duplicates in import (set-semantics) during slow import', async() => {
+    const match = store.match();
+
+    const importStream = new Readable({ objectMode: true });
+    importStream._read = () => {
+      setImmediate(() => {
+        importStream.push(quad('s1', 'p1', 'o1'));
+      });
+      setImmediate(() => {
+        importStream.push(quad('s1', 'p1', 'o1'));
+      });
+      setImmediate(() => {
+        importStream.push(null);
+      });
+    };
+    store.import(importStream);
+    await new Promise(resolve => importStream.on('end', resolve));
+    store.end();
+
+    expect(await arrayifyStream(match)).toEqualRdfQuadArray(
+      [ quad('s1', 'p1', 'o1') ],
+    );
+  });
+
+  it('handles errors in import', async() => {
+    const importStream = new PassThrough({ objectMode: true });
+    const returnStream = store.import(importStream);
+    const error = new Error('myError');
+    const callback = jest.fn();
+
+    returnStream.on('error', callback);
+    importStream.emit('error', error);
+
+    expect(callback).toHaveBeenCalled();
+    expect(callback).toHaveBeenCalledWith(error);
+    store.end();
+  });
 });