diff --git a/include/haproxy/htx-t.h b/include/haproxy/htx-t.h
index d9c08c8..d57404a 100644
--- a/include/haproxy/htx-t.h
+++ b/include/haproxy/htx-t.h
@@ -145,7 +145,9 @@
 #define HTX_FL_PROCESSING_ERROR  0x00000002 /* Set when a processing error occurred */
 #define HTX_FL_UPGRADE           0x00000004 /* Set when an upgrade is in progress */
 #define HTX_FL_PROXY_RESP        0x00000008 /* Set when the response was generated by HAProxy */
-
+#define HTX_FL_EOI               0x00000010 /* Set when end-of-input is reached from the HTX point of view
+					     * (at worst, on the EOM block is missing)
+					     */
 
 /* HTX block's type (max 15). */
 enum htx_blk_type {
diff --git a/include/haproxy/htx.h b/include/haproxy/htx.h
index a849f12..5ede1a3 100644
--- a/include/haproxy/htx.h
+++ b/include/haproxy/htx.h
@@ -585,6 +585,15 @@
 	return (htx->head != -1);
 }
 
+/* Returns 1 if no more data are expected for the message <htx>. Otherwise it
+ * returns 0. Note that it is illegal to call this with htx == NULL. Note also
+ * the EOM block may be missing.
+ */
+static inline int htx_expect_more(const struct htx *htx)
+{
+	return !(htx->flags & HTX_FL_EOI);
+}
+
 /* Copy an HTX message stored in the buffer <msg> to <htx>. We take care to
  * not overwrite existing data. All the message is copied or nothing. It returns
  * 1 on success and 0 on error.
diff --git a/src/cache.c b/src/cache.c
index 6fc1c14..533b902 100644
--- a/src/cache.c
+++ b/src/cache.c
@@ -926,6 +926,7 @@
 	}
 
 	if (appctx->st0 == HTX_CACHE_EOM) {
+		res_htx->flags |= HTX_FL_EOI; /* no more data are expected. Only EOM remains to add now */
 		if (!htx_add_endof(res_htx, HTX_BLK_EOM)) {
 			si_rx_room_blk(si);
 			goto out;
diff --git a/src/h1_htx.c b/src/h1_htx.c
index 351980b..a2ee510 100644
--- a/src/h1_htx.c
+++ b/src/h1_htx.c
@@ -616,6 +616,8 @@
 		dsthtx->flags |= HTX_FL_PARSING_ERROR;
 		return 0;
 	}
+
+	dsthtx->flags |= HTX_FL_EOI; /* no more data are expected. Only EOM remains to add now */
 	if (max < sizeof(struct htx_blk) + 1 || !htx_add_endof(dsthtx, HTX_BLK_EOM))
 		return 0;
 
diff --git a/src/hlua.c b/src/hlua.c
index 254c2a3..556de42 100644
--- a/src/hlua.c
+++ b/src/hlua.c
@@ -4582,6 +4582,7 @@
 	}
 
 	/* Finalize headers. */
+	htx->flags |= HTX_FL_EOI; /* no more data are expected. Only EOM remains to add now */
 	if (!htx_add_endof(htx, HTX_BLK_EOH)) {
 		hlua_pusherror(L, "Lua applet http '%s': Failed create the response.\n",
 			       appctx->appctx->rule->arg.hlua_rule->fcn.name);
diff --git a/src/http_ana.c b/src/http_ana.c
index b77bf2a..7c1a1a1 100644
--- a/src/http_ana.c
+++ b/src/http_ana.c
@@ -4577,6 +4577,7 @@
 		channel_auto_close(res);
 		channel_shutr_now(res);
 		res->flags |= CF_EOI; /* The response is terminated, add EOI */
+		htxbuf(&res->buf)->flags |= HTX_FL_EOI; /* no more data are expected */
 	}
 	else {
 		/* Send ASAP informational messages. Rely on CF_EOI for final
diff --git a/src/mux_h2.c b/src/mux_h2.c
index 4b790e6..44955ba 100644
--- a/src/mux_h2.c
+++ b/src/mux_h2.c
@@ -4452,6 +4452,7 @@
 
 	if ((h2c->dff & H2_F_HEADERS_END_STREAM)) {
 		/* Mark the end of message using EOM */
+		htx->flags |= HTX_FL_EOI; /* no more data are expected. Only EOM remains to add now */
 		if (!htx_add_endof(htx, HTX_BLK_EOM)) {
 			TRACE_STATE("failed to append HTX EOM block into rxbuf", H2_EV_RX_FRAME|H2_EV_RX_HDR|H2_EV_H2S_ERR, h2c->conn);
 			goto fail;
@@ -4587,6 +4588,7 @@
 	 */
 
 	if (h2c->dff & H2_F_DATA_END_STREAM) {
+		htx->flags |= HTX_FL_EOI; /* no more data are expected. Only EOM remains to add now */
 		if (!htx_add_endof(htx, HTX_BLK_EOM)) {
 			TRACE_STATE("h2s rxbuf is full, failed to add EOM", H2_EV_RX_FRAME|H2_EV_RX_DATA|H2_EV_H2S_BLK, h2c->conn, h2s);
 			h2c->flags |= H2_CF_DEM_SFULL;
@@ -5778,6 +5780,8 @@
 		if (htx_is_empty(buf_htx))
 			cs->flags |= CS_FL_EOI;
 	}
+	else if (htx_is_empty(h2s_htx))
+		buf_htx->flags |= (h2s_htx->flags & HTX_FL_EOI);
 
 	buf_htx->extra = (h2s_htx->extra ? (h2s_htx->data + h2s_htx->extra) : 0);
 	htx_to_buf(buf_htx, buf);
diff --git a/src/stats.c b/src/stats.c
index d69c764..562cd82 100644
--- a/src/stats.c
+++ b/src/stats.c
@@ -3339,6 +3339,7 @@
 
 	if (appctx->st0 == STAT_HTTP_DONE) {
 		/* Don't add TLR because mux-h1 will take care of it */
+		res_htx->flags |= HTX_FL_EOI; /* no more data are expected. Only EOM remains to add now */
 		if (!htx_add_endof(res_htx, HTX_BLK_EOM)) {
 			si_rx_room_blk(si);
 			goto out;
diff --git a/src/tcpcheck.c b/src/tcpcheck.c
index e83b915..fc64a10 100644
--- a/src/tcpcheck.c
+++ b/src/tcpcheck.c
@@ -1335,8 +1335,11 @@
 
 
 		if (!htx_add_endof(htx, HTX_BLK_EOH) ||
-		    (istlen(body) && !htx_add_data_atonce(htx, body)) ||
-		    !htx_add_endof(htx, HTX_BLK_EOM))
+		    (istlen(body) && !htx_add_data_atonce(htx, body)))
+			goto error_htx;
+
+		htx->flags |= HTX_FL_EOI; /* no more data are expected. Only EOM remains to add now */
+		if (!htx_add_endof(htx, HTX_BLK_EOM))
 			goto error_htx;
 
 		htx_to_buf(htx, &check->bo);