diff --git a/openml/tasks/functions.py b/openml/tasks/functions.py
index 25156f2e5..c4bb13617 100644
--- a/openml/tasks/functions.py
+++ b/openml/tasks/functions.py
@@ -492,6 +492,7 @@ def _create_task_from_xml(xml: str) -> OpenMLTask:
         "data_set_id": inputs["source_data"]["oml:data_set"]["oml:data_set_id"],
         "evaluation_measure": evaluation_measures,
     }
+    # TODO: add OpenMLClusteringTask?
     if task_type in (
         TaskType.SUPERVISED_CLASSIFICATION,
         TaskType.SUPERVISED_REGRESSION,
@@ -508,6 +509,10 @@ def _create_task_from_xml(xml: str) -> OpenMLTask:
         common_kwargs["estimation_procedure_type"] = inputs["estimation_procedure"][
             "oml:estimation_procedure"
         ]["oml:type"]
+        common_kwargs["estimation_procedure_id"] = int(
+            inputs["estimation_procedure"]["oml:estimation_procedure"]["oml:id"]
+        )
+
         common_kwargs["estimation_parameters"] = estimation_parameters
         common_kwargs["target_name"] = inputs["source_data"]["oml:data_set"]["oml:target_feature"]
         common_kwargs["data_splits_url"] = inputs["estimation_procedure"][
diff --git a/tests/test_tasks/test_classification_task.py b/tests/test_tasks/test_classification_task.py
index bb4545154..d3553262f 100644
--- a/tests/test_tasks/test_classification_task.py
+++ b/tests/test_tasks/test_classification_task.py
@@ -15,7 +15,7 @@ def setUp(self, n_levels: int = 1):
         super().setUp()
         self.task_id = 119  # diabetes
         self.task_type = TaskType.SUPERVISED_CLASSIFICATION
-        self.estimation_procedure = 1
+        self.estimation_procedure = 5
 
     def test_get_X_and_Y(self):
         X, Y = super().test_get_X_and_Y()
@@ -30,7 +30,8 @@ def test_download_task(self):
         assert task.task_id == self.task_id
         assert task.task_type_id == TaskType.SUPERVISED_CLASSIFICATION
         assert task.dataset_id == 20
+        assert task.estimation_procedure_id == self.estimation_procedure
 
     def test_class_labels(self):
         task = get_task(self.task_id)
-        assert task.class_labels == ["tested_negative", "tested_positive"]
+        assert task.class_labels == ["tested_negative", "tested_positive"]
\ No newline at end of file
diff --git a/tests/test_tasks/test_regression_task.py b/tests/test_tasks/test_regression_task.py
index 36decc534..14ed59470 100644
--- a/tests/test_tasks/test_regression_task.py
+++ b/tests/test_tasks/test_regression_task.py
@@ -18,11 +18,11 @@ class OpenMLRegressionTaskTest(OpenMLSupervisedTaskTest):
 
     def setUp(self, n_levels: int = 1):
         super().setUp()
-
+        self.estimation_procedure = 9
         task_meta_data = {
             "task_type": TaskType.SUPERVISED_REGRESSION,
             "dataset_id": 105,  # wisconsin
-            "estimation_procedure_id": 7,
+            "estimation_procedure_id": self.estimation_procedure, # non default value to test estimation procedure id
             "target_name": "time",
         }
         _task_id = check_task_existence(**task_meta_data)
@@ -46,7 +46,7 @@ def setUp(self, n_levels: int = 1):
                     raise Exception(repr(e))
         self.task_id = task_id
         self.task_type = TaskType.SUPERVISED_REGRESSION
-        self.estimation_procedure = 7
+
 
     def test_get_X_and_Y(self):
         X, Y = super().test_get_X_and_Y()
@@ -61,3 +61,4 @@ def test_download_task(self):
         assert task.task_id == self.task_id
         assert task.task_type_id == TaskType.SUPERVISED_REGRESSION
         assert task.dataset_id == 105
+        assert task.estimation_procedure_id == self.estimation_procedure