diff --git a/packages/stlite-kernel/src/index.ts b/packages/stlite-kernel/src/index.ts
index dd0c0aadc..cd8b57797 100644
--- a/packages/stlite-kernel/src/index.ts
+++ b/packages/stlite-kernel/src/index.ts
@@ -1,5 +1,4 @@
 export * from "./kernel";
 export * from "./streamlit-replacements/lib/ConnectionManager";
-export * from "./streamlit-replacements/lib/ConnectionState";
 export * from "./streamlit-replacements/lib/FileUploadClient";
 export * from "./react-helpers";
diff --git a/packages/stlite-kernel/src/streamlit-replacements/lib/ConnectionManager.ts b/packages/stlite-kernel/src/streamlit-replacements/lib/ConnectionManager.ts
index 77308e0ef..0d856dda5 100644
--- a/packages/stlite-kernel/src/streamlit-replacements/lib/ConnectionManager.ts
+++ b/packages/stlite-kernel/src/streamlit-replacements/lib/ConnectionManager.ts
@@ -1,14 +1,20 @@
 // Mimic https://github.com/streamlit/streamlit/blob/1.9.0/frontend/src/lib/ConnectionManager.ts
+// and WebsocketConnection.
 
 import { BackMsg, ForwardMsg } from "streamlit-browser/src/autogen/proto"
 import { BaseUriParts } from "streamlit-browser/src/lib/UriUtil"
 import { ReactNode } from "react"
 
 import { StliteKernel } from "../../kernel"
-import { ConnectionState } from "./ConnectionState"
+import { ConnectionState } from "streamlit-browser/src/lib/ConnectionState"
+import { ForwardMsgCache } from "streamlit-browser/src/lib/ForwardMessageCache"
 import { ensureError } from "streamlit-browser/src/lib/ErrorHandling"
 import { DUMMY_BASE_HOSTNAME, DUMMY_BASE_PORT } from "../../consts"
 
+interface MessageQueue {
+  [index: number]: any
+}
+
 interface Props {
   /**
    * Kernel object to connect to.
@@ -38,13 +44,14 @@ export class ConnectionManager {
 
   constructor(props: Props) {
     this.props = props
+    this.cache = new ForwardMsgCache(() => this.getBaseUriParts())
 
     this.props.kernel.onWebSocketMessage((payload) => {
       if (typeof payload === "string") {
         console.error("Unexpected payload type.")
         return
       }
-      props.onMessage(ForwardMsg.decode(payload))
+      this.handleMessage(payload)
     })
 
     this.props.kernel.loaded.then(() => {
@@ -94,12 +101,60 @@ export class ConnectionManager {
     }
   }
 
+  /**
+   * ForwardMessages get passed through this cache. This gets initialized
+   * once we connect to the server.
+   */
+  private readonly cache: ForwardMsgCache
+
+  /**
+   * To guarantee packet transmission order, this is the index of the last
+   * dispatched incoming message.
+   */
+  private lastDispatchedMessageIndex = -1
+
+  /**
+   * And this is the index of the next message we receive.
+   */
+  private nextMessageIndex = 0
+
+  /**
+   * This dictionary stores received messages that we haven't sent out yet
+   * (because we're still decoding previous messages)
+   */
+  private readonly messageQueue: MessageQueue = {}
+
   /**
    * Increment the runCount on our message cache, and clear entries
    * whose age is greater than the max.
    */
   public incrementMessageCacheRunCount(maxMessageAge: number): void {
-    // TODO: Implement
+    this.cache.incrementRunCount(maxMessageAge)
+  }
+
+  private async handleMessage(data: ArrayBuffer): Promise<void> {
+    // Assign this message an index.
+    const messageIndex = this.nextMessageIndex
+    this.nextMessageIndex += 1
+
+    const encodedMsg = new Uint8Array(data)
+    const msg = ForwardMsg.decode(encodedMsg)
+
+    this.messageQueue[messageIndex] = await this.cache.processMessagePayload(
+      msg,
+      encodedMsg
+    )
+
+    // Dispatch any pending messages in the queue. This may *not* result
+    // in our just-decoded message being dispatched: if there are other
+    // messages that were received earlier than this one but are being
+    // downloaded, our message won't be sent until they're done.
+    while (this.lastDispatchedMessageIndex + 1 in this.messageQueue) {
+      const dispatchMessageIndex = this.lastDispatchedMessageIndex + 1
+      this.props.onMessage(this.messageQueue[dispatchMessageIndex])
+      delete this.messageQueue[dispatchMessageIndex]
+      this.lastDispatchedMessageIndex = dispatchMessageIndex
+    }
   }
 
   private async connect(): Promise<void> {
diff --git a/packages/stlite-kernel/src/streamlit-replacements/lib/ConnectionState.ts b/packages/stlite-kernel/src/streamlit-replacements/lib/ConnectionState.ts
deleted file mode 100644
index 8ac110f2c..000000000
--- a/packages/stlite-kernel/src/streamlit-replacements/lib/ConnectionState.ts
+++ /dev/null
@@ -1,24 +0,0 @@
-/**
- * @license
- * Copyright 2018-2022 Streamlit Inc.
- *
- * Licensed under the Apache License, Version 2.0 (the "License");
- * you may not use this file except in compliance with the License.
- * You may obtain a copy of the License at
- *
- *    http://www.apache.org/licenses/LICENSE-2.0
- *
- * Unless required by applicable law or agreed to in writing, software
- * distributed under the License is distributed on an "AS IS" BASIS,
- * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
- * See the License for the specific language governing permissions and
- * limitations under the License.
- */
-
-export enum ConnectionState {
-  CONNECTED = "CONNECTED",
-  DISCONNECTED_FOREVER = "DISCONNECTED_FOREVER",
-  INITIAL = "INITIAL",
-  PINGING_SERVER = "PINGING_SERVER",
-  CONNECTING = "CONNECTING",
-}