diff --git a/src/ol/format/GML3.js b/src/ol/format/GML3.js
index e1d6a878d0..3cca0a2a47 100644
--- a/src/ol/format/GML3.js
+++ b/src/ol/format/GML3.js
@@ -13,6 +13,7 @@ import {
   XML_SCHEMA_INSTANCE_URI,
   createElementNS,
   getAllTextContent,
+  makeArrayExtender,
   makeArrayPusher,
   makeChildAppender,
   makeReplacer,
@@ -189,13 +190,7 @@ class GML3 extends GMLBase {
    * @return {Array<number>|undefined} flat coordinates.
    */
   readSegment(node, objectStack) {
-    return pushParseAndPop(
-      [null],
-      this.SEGMENTS_PARSERS,
-      node,
-      objectStack,
-      this
-    );
+    return pushParseAndPop([], this.SEGMENTS_PARSERS, node, objectStack, this);
   }
 
   /**
@@ -1161,7 +1156,9 @@ GML3.prototype.PATCHES_PARSERS = {
  */
 GML3.prototype.SEGMENTS_PARSERS = {
   'http://www.opengis.net/gml': {
-    'LineStringSegment': makeReplacer(GML3.prototype.readLineStringSegment),
+    'LineStringSegment': makeArrayExtender(
+      GML3.prototype.readLineStringSegment
+    ),
   },
 };
 
diff --git a/src/ol/format/GML32.js b/src/ol/format/GML32.js
index 193d9b2378..6519564e99 100644
--- a/src/ol/format/GML32.js
+++ b/src/ol/format/GML32.js
@@ -169,7 +169,9 @@ GML32.prototype.PATCHES_PARSERS = {
  */
 GML32.prototype.SEGMENTS_PARSERS = {
   'http://www.opengis.net/gml/3.2': {
-    'LineStringSegment': makeReplacer(GML3.prototype.readLineStringSegment),
+    'LineStringSegment': makeArrayExtender(
+      GML3.prototype.readLineStringSegment
+    ),
   },
 };
 
diff --git a/test/browser/spec/ol/format/gml.test.js b/test/browser/spec/ol/format/gml.test.js
index 3c28d0c46e..d793d26be4 100644
--- a/test/browser/spec/ol/format/gml.test.js
+++ b/test/browser/spec/ol/format/gml.test.js
@@ -2252,6 +2252,44 @@ describe('ol.format.GML32', function () {
         const serialized = format.writeGeometryNode(g);
         expect(serialized.firstElementChild).to.xmleql(parse(text));
       });
+
+      it('can read and write a curve geometry', function () {
+        const text =
+          '<gml:Curve xmlns:gml="http://www.opengis.net/gml/3.2" ' +
+          '    srsName="CRS:84">' +
+          '  <gml:segments>' +
+          '    <gml:LineStringSegment>' +
+          '      <gml:posList srsDimension="2">1 2 3 4</gml:posList>' +
+          '    </gml:LineStringSegment>' +
+          '    <gml:LineStringSegment>' +
+          '      <gml:posList srsDimension="2">5 6 7 8</gml:posList>' +
+          '    </gml:LineStringSegment>' +
+          '  </gml:segments>' +
+          '</gml:Curve>';
+        const g = readGeometry(format, text);
+        expect(g).to.be.an(LineString);
+        expect(g.getCoordinates()).to.eql([
+          [1, 2, 0],
+          [3, 4, 0],
+          [5, 6, 0],
+          [7, 8, 0],
+        ]);
+        format = new GML32({srsName: 'CRS:84', curve: true});
+        const serialized = format.writeGeometryNode(g);
+        // Conversion back to GML is not lossless, because we don't know
+        // the mapping of original LineString segements to the OpenLayers
+        // LineString geometry's coordinates.
+        const expected =
+          '<gml:Curve xmlns:gml="http://www.opengis.net/gml/3.2" ' +
+          '    srsName="CRS:84">' +
+          '  <gml:segments>' +
+          '    <gml:LineStringSegment>' +
+          '      <gml:posList srsDimension="2">1 2 3 4 5 6 7 8</gml:posList>' +
+          '    </gml:LineStringSegment>' +
+          '  </gml:segments>' +
+          '</gml:Curve>';
+        expect(serialized.firstElementChild).to.xmleql(parse(expected));
+      });
     });
 
     describe('envelope', function () {