diff --git a/src/parser.cpp b/src/parser.cpp
index 3060c83f9..04f140841 100644
--- a/src/parser.cpp
+++ b/src/parser.cpp
@@ -1109,7 +1109,7 @@ void Parser::ParserImpl::loadConnection(const ModelPtr &model, const XmlNodePtr
             issue->mPimpl->setReferenceRule(Issue::ReferenceRule::CONNECTION_EXCLUDE_SELF);
             addIssue(issue);
         } else {
-            if (component1Name > component2Name) {
+            if (!mParsing1XVersion && (component1Name > component2Name)) {
                 std::string tmp = component1Name;
                 component1Name = component2Name;
                 component2Name = tmp;
diff --git a/tests/connection/connection.cpp b/tests/connection/connection.cpp
index 76fda64dd..abefc260c 100644
--- a/tests/connection/connection.cpp
+++ b/tests/connection/connection.cpp
@@ -1588,3 +1588,11 @@ TEST(Connection, sameNamedVariablesInDifferentComponents)
 
     EXPECT_EQ(size_t(0), p->issueCount());
 }
+
+TEST(Connection, mapComponentsAreOrderDependentInCellML1X)
+{
+    auto p = libcellml::Parser::create(false);
+    auto m = p->parseModel(fileContents("cellml1X/map_components.cellml"));
+
+    EXPECT_EQ(size_t(0), p->errorCount());
+}
diff --git a/tests/resources/cellml1X/map_components.cellml b/tests/resources/cellml1X/map_components.cellml
new file mode 100644
index 000000000..7de46b31c
--- /dev/null
+++ b/tests/resources/cellml1X/map_components.cellml
@@ -0,0 +1,30 @@
+<?xml version='1.0' encoding='utf-8'?>
+<model xmlns="http://www.cellml.org/cellml/1.0#" xmlns:cellml="http://www.cellml.org/cellml/1.0#" name="map_components">
+  <units name="molar">
+    <unit units="mole"/>
+    <unit units="litre" exponent="-1"/>
+  </units>
+  <units name="micromolar">
+    <unit units="molar" prefix="micro"/>
+  </units>
+  <component name="R">
+    <variable units="micromolar" public_interface="out" name="R" initial_value="0.001"/>
+    <variable units="micromolar" public_interface="out" name="D" initial_value="0.01"/>
+    <variable units="micromolar" public_interface="in" name="DR"/>
+  </component>
+  <component name="DR">
+    <variable units="micromolar" public_interface="in" name="D" initial_value=""/>
+    <variable units="micromolar" public_interface="in" name="R" initial_value=""/>
+    <variable units="micromolar" public_interface="out" name="DR"/>
+  </component>
+  <connection>
+    <map_components component_2="R" component_1="DR"/>
+    <map_variables variable_2="DR" variable_1="DR"/>
+  </connection>
+  <connection>
+    <map_components component_2="DR" component_1="R"/>
+    <map_variables variable_2="R" variable_1="R"/>
+    <map_variables variable_2="D" variable_1="D"/>
+  </connection>
+ </model>
+