diff --git a/Tests/NumLib/TestFixedTimeStepping.cpp b/Tests/NumLib/TestFixedTimeStepping.cpp
new file mode 100644
index 0000000000000000000000000000000000000000..503777e8a16c1f0ecd0956b153ca3b22d6bb19cc
--- /dev/null
+++ b/Tests/NumLib/TestFixedTimeStepping.cpp
@@ -0,0 +1,144 @@
+/**
+ * \file
+ * \copyright
+ * Copyright (c) 2012-2024, OpenGeoSys Community (http://www.opengeosys.org)
+ *            Distributed under a Modified BSD License.
+ *              See accompanying file LICENSE.txt or
+ *              http://www.opengeosys.org/project/license
+ *
+ */
+
+#include <gtest/gtest.h>
+
+#include <autocheck/autocheck.hpp>
+#include <numeric>
+
+#include "NumLib/TimeStepping/Algorithms/FixedTimeStepping.h"
+
+namespace ac = autocheck;
+
+class NumLibFixedTimeStepping : public ::testing::Test
+{
+public:
+    NumLibFixedTimeStepping()
+    {
+        double_classifier.trivial([](const std::vector<double>& time_step_sizes)
+                                  { return time_step_sizes.empty(); });
+        double_classifier.collect(
+            [](const std::vector<double>& time_step_sizes)
+            {
+                return time_step_sizes.size() == 1
+                           ? "of test cases with one time step size"
+                           : "of test cases with more than one time step size "
+                             "entry";
+            });
+
+        pair_classifier.trivial(
+            [](const std::vector<NumLib::RepeatDtPair>& pairs)
+            { return pairs.size() == 1; });
+        pair_classifier.collect(
+            [](const std::vector<NumLib::RepeatDtPair>& pairs)
+            {
+                return pairs.size() == 1
+                           ? "of test cases with one pair of RepeatDtPair"
+                           : "of test cases with more than one pair of "
+                             "RepeatDtPair";
+            });
+    }
+
+protected:
+    ac::gtest_reporter gtest_reporter;
+    ac::classifier<std::vector<double>> double_classifier;
+    ac::classifier<std::vector<NumLib::RepeatDtPair>> pair_classifier;
+};
+
+TEST_F(NumLibFixedTimeStepping, EmptyRepeatDtPairs)
+{
+    std::vector<NumLib::RepeatDtPair> empty;
+    ASSERT_FALSE(NumLib::FixedTimeStepping::areRepeatDtPairsValid(empty));
+}
+
+TEST_F(NumLibFixedTimeStepping, RepeatZeroDtPairs)
+{
+    std::vector<NumLib::RepeatDtPair> zero_repeat_dt_pair_vec{{0, 1.0}};
+    ASSERT_FALSE(NumLib::FixedTimeStepping::areRepeatDtPairsValid(
+        zero_repeat_dt_pair_vec));
+}
+
+std::vector<double> transformTimesToDts(std::vector<double> const& times)
+{
+    std::vector<double> dts(times.size());
+    std::adjacent_difference(times.begin(), times.end(), dts.begin());
+    return dts;
+}
+
+std::vector<NumLib::RepeatDtPair> transformToRepeatDtPair(
+    std::vector<double> const& dts)
+{
+    std::vector<NumLib::RepeatDtPair> repeat_dt_pairs;
+    std::transform(dts.begin(),
+                   dts.end(),
+                   std::back_inserter(repeat_dt_pairs),
+                   [](auto const dt) { return std::tuple(1, dt); });
+    return repeat_dt_pairs;
+}
+
+TEST_F(NumLibFixedTimeStepping, next)
+{
+    auto test = [](std::vector<double>& expected_time_points) -> bool
+    {
+        double const t_initial = expected_time_points.front();
+
+        expected_time_points.erase(expected_time_points.begin());
+
+        double const t_end = expected_time_points.back();
+        auto dts = transformTimesToDts(expected_time_points);
+        dts.front() -= t_initial;
+        auto const repeat_dt_pair = transformToRepeatDtPair(dts);
+        NumLib::FixedTimeStepping fixed_time_stepping{
+            t_initial, t_end, repeat_dt_pair, {}};
+
+        NumLib::TimeStep ts_dummy(0, 0, 0);
+        NumLib::TimeStep ts_current(0, t_initial, 0);
+        for (auto const& expected_time_point : expected_time_points)
+        {
+            auto [is_next, step_size] =
+                fixed_time_stepping.next(0.0 /* solution_error */,
+                                         0 /* number_of_iterations */,
+                                         ts_dummy,
+                                         ts_current);
+            // this only happens if the last time step was processed or the
+            // current time is already at the end time up to machine precision
+            if (!is_next && step_size != 0.0)
+            {
+                return false;
+            }
+            // if the current time plus the computed step size minus the
+            // expected time is larger than the minimal time step size then the
+            // step size should be larger
+            // if next is true then the step
+            if (is_next && std::abs((ts_current.current() + step_size) -
+                                    expected_time_point) >
+                               NumLib::TimeStep::minimalTimeStepSize)
+            {
+                return false;
+            }
+            // if next is true then the step size should be larger than zero
+            if (is_next && step_size == 0.0)
+            {
+                return false;
+            }
+            ts_current += step_size;
+        }
+        return ts_current.timeStepNumber() == dts.size();
+    };
+
+    auto ordered_list_generator = ac::ordered_list(ac::generator<double>());
+    auto time_points = ac::make_arbitrary(ordered_list_generator);
+    // generated list must not be empty
+    time_points.discard_if([](std::vector<double> const& xs)
+                           { return xs.size() <= 1; });
+
+    ac::check<std::vector<double>>(
+        test, 1000, time_points, gtest_reporter, double_classifier);
+}