diff --git a/sksurv/nonparametric.py b/sksurv/nonparametric.py
index 82ae7364..d1ff3240 100644
--- a/sksurv/nonparametric.py
+++ b/sksurv/nonparametric.py
@@ -284,7 +284,13 @@ def kaplan_meier_estimator(
            Survival Function Based on Transformations", Scandinavian Journal of
            Statistics. 1990;17(1):35–41.
     """
-    event, time_enter, time_exit = check_y_survival(event, time_enter, time_exit, allow_all_censored=True)
+    event, time_enter, time_exit = check_y_survival(
+        event,
+        time_enter,
+        time_exit,
+        allow_all_censored=True,
+        allow_time_zero=reverse or time_enter is not None,
+    )
     check_consistent_length(event, time_enter, time_exit)
 
     if conf_type is not None and reverse:
diff --git a/sksurv/svm/survival_svm.py b/sksurv/svm/survival_svm.py
index 0103f7a4..7d8b7ff2 100644
--- a/sksurv/svm/survival_svm.py
+++ b/sksurv/svm/survival_svm.py
@@ -758,9 +758,6 @@ def fit(self, X, y):
             if self.optimizer in {"simple", "PRSVM"}:
                 raise ValueError(f"optimizer {self.optimizer!r} does not implement regression objective")
 
-            if (time <= 0).any():
-                raise ValueError("observed time contains values smaller or equal to zero")
-
             # log-transform time
             time = np.log(time)
             assert np.isfinite(time).all()
diff --git a/sksurv/util.py b/sksurv/util.py
index ba764aff..25305f6f 100644
--- a/sksurv/util.py
+++ b/sksurv/util.py
@@ -96,7 +96,7 @@ def from_dataframe(event, time, data):
         )
 
 
-def check_y_survival(y_or_event, *args, allow_all_censored=False):
+def check_y_survival(y_or_event, *args, allow_all_censored=False, allow_time_zero=False):
     """Check that array correctly represents an outcome for survival analysis.
 
     Parameters
@@ -114,6 +114,9 @@ def check_y_survival(y_or_event, *args, allow_all_censored=False):
     allow_all_censored : bool, optional, default: False
         Whether to allow all events to be censored.
 
+    allow_time_zero : bool, optional, default: False
+        Whether to allow event times to be zero.
+
     Returns
     -------
     event : array, shape=[n_samples,], dtype=bool
@@ -156,6 +159,15 @@ def check_y_survival(y_or_event, *args, allow_all_censored=False):
         if not np.issubdtype(yt.dtype, np.number):
             raise ValueError(f"time must be numeric, but found {yt.dtype} for argument {i + 2}")
 
+        if allow_time_zero:
+            cond = yt < 0
+            msg = "observed time contains values smaller zero"
+        else:
+            cond = yt <= 0
+            msg = "observed time contains values smaller or equal to zero"
+        if np.any(cond):
+            raise ValueError(msg)
+
         return_val.append(yt)
 
     return tuple(return_val)
diff --git a/tests/test_metrics.py b/tests/test_metrics.py
index ec54a857..85169173 100644
--- a/tests/test_metrics.py
+++ b/tests/test_metrics.py
@@ -1075,7 +1075,7 @@ def test_brier_coxph():
 
 
 def test_brier_score_int_dtype():
-    times = np.arange(30, dtype=int)
+    times = np.arange(1, 31, dtype=int)
     rnd = np.random.RandomState(1)
     times = rnd.choice(times, 20)
 
diff --git a/tests/test_survival_function.py b/tests/test_survival_function.py
index 5449700a..2d08d71c 100644
--- a/tests/test_survival_function.py
+++ b/tests/test_survival_function.py
@@ -4,6 +4,7 @@
 
 from sksurv.linear_model import CoxnetSurvivalAnalysis
 from sksurv.testing import all_survival_estimators
+from sksurv.util import Surv
 
 
 def all_survival_function_estimators():
@@ -30,3 +31,13 @@ def test_survival_functions(estimator, make_whas500):
     arr = np.row_stack([fn(times) for fn in fns_cls])
 
     assert_array_almost_equal(arr, fns_arr)
+
+
+@pytest.mark.parametrize("estimator", all_survival_function_estimators())
+@pytest.mark.parametrize("y_time", [-1e-8, -1, np.finfo(float).min])
+def test_fit_negative_survial_time_raises(estimator, y_time):
+    X = np.random.randn(7, 3)
+    y = Surv.from_arrays(event=np.ones(7, dtype=bool), time=[1, 9, 3, y_time, 1, 8, 1e10])
+
+    with pytest.raises(ValueError, match="observed time contains values smaller or equal to zero"):
+        estimator.fit(X, y)