diff --git a/changes/9625.combine_1d.rst b/changes/9625.combine_1d.rst
new file mode 100644
index 0000000000..f829b9fb75
--- /dev/null
+++ b/changes/9625.combine_1d.rst
@@ -0,0 +1 @@
+Allow all-NaN spectra to be skipped instead of causing crashes
diff --git a/jwst/combine_1d/combine1d.py b/jwst/combine_1d/combine1d.py
index 1aa06a376c..cc316fe38f 100644
--- a/jwst/combine_1d/combine1d.py
+++ b/jwst/combine_1d/combine1d.py
@@ -727,6 +727,12 @@ def _read_input_spectra(input_model, exptime_key, input_spectra):
     else:
         spectra = input_model.spec
     for in_spec in spectra:
+        if not np.any(np.isfinite(in_spec.spec_table.field("flux"))):
+            log.warning(
+                f"Input spectrum {in_spec.source_id} order {in_spec.spectral_order} "
+                f"from group_id {in_spec.meta.group_id} has no valid flux values; skipping."
+            )
+            continue
         spectral_order = in_spec.spectral_order
         if spectral_order not in input_spectra:
             input_spectra[spectral_order] = []
@@ -768,6 +774,12 @@ def combine_1d_spectra(input_model, exptime_key, sigma_clip=None):
     else:
         _read_input_spectra(input_model, exptime_key, input_spectra)
 
+    if len(input_spectra) == 0:
+        log.error("No valid input spectra found for source. Skipping.")
+        result = input_model.copy()
+        result.meta.cal_step.combine_1d = "SKIPPED"
+        return result
+
     for order in input_spectra:
         output_spectra[order] = OutputSpectrumModel()
         output_spectra[order].assign_wavelengths(input_spectra[order])
diff --git a/jwst/combine_1d/combine_1d_step.py b/jwst/combine_1d/combine_1d_step.py
index c9ac222c65..1948c6b04d 100644
--- a/jwst/combine_1d/combine_1d_step.py
+++ b/jwst/combine_1d/combine_1d_step.py
@@ -71,7 +71,15 @@ def process(self, input_data):
                         result = combine1d.combine_1d_spectra(
                             model, self.exptime_key, sigma_clip=self.sigma_clip
                         )
-                        results_list.append(result)
+                        if not result.meta.cal_step.combine_1d == "SKIPPED":
+                            results_list.append(result)
+                    if not results_list:
+                        self.log.error(
+                            "No valid input spectra found in WFSSMultiSpecModel. Skipping."
+                        )
+                        result = input_model.copy()
+                        result.meta.cal_step.combine_1d = "SKIPPED"
+                        return result
                     result = make_wfss_multicombined(results_list)
                     result.meta.cal_step.combine_1d = "COMPLETE"
                     return result
diff --git a/jwst/combine_1d/tests/test_combine1d.py b/jwst/combine_1d/tests/test_combine1d.py
index d7ff2fd994..100913afba 100644
--- a/jwst/combine_1d/tests/test_combine1d.py
+++ b/jwst/combine_1d/tests/test_combine1d.py
@@ -2,6 +2,8 @@
 
 import numpy as np
 import pytest
+import logging
+from jwst.tests.helpers import LogWatcher
 
 from jwst import datamodels
 
@@ -227,3 +229,35 @@ def test_wfss_multi_input(wfss_multiexposure):
     assert np.all(tab["SOURCE_TYPE"] == "POINT")
 
     assert result.spec[0].dispersion_direction == 3
+
+
+def test_allnan_skip(wfss_multiexposure, monkeypatch):
+    """Test that all-nan spectra are skipped."""
+    # Set all flux values to NaN
+    for spec in wfss_multiexposure.spec:
+        spec.spec_table["FLUX"][:] = np.nan
+
+    # message when a single spectrum has no valid flux values
+    watcher0 = LogWatcher(
+        "Input spectrum 5 order 1 from group_id 1 has no valid flux values; skipping."
+    )
+    monkeypatch.setattr(logging.getLogger("jwst.combine_1d.combine1d"), "warning", watcher0)
+    result = Combine1dStep.call(wfss_multiexposure)
+    assert result.meta.cal_step.combine_1d == "SKIPPED"
+    watcher0.assert_seen()
+
+    # check for the other log messages
+    # these must be done one at a time because the watcher can only be monkeypatched once
+    # message when no valid input spectra are found for the source
+    watcher1 = LogWatcher("No valid input spectra found for source. Skipping.")
+    monkeypatch.setattr(logging.getLogger("jwst.combine_1d.combine1d"), "error", watcher1)
+    result = Combine1dStep.call(wfss_multiexposure)
+    assert result.meta.cal_step.combine_1d == "SKIPPED"
+    watcher1.assert_seen()
+
+    # message when no valid input spectra at all are found
+    watcher2 = LogWatcher("No valid input spectra found in WFSSMultiSpecModel")
+    monkeypatch.setattr(logging.getLogger("stpipe.Combine1dStep"), "error", watcher2)
+    result = Combine1dStep.call(wfss_multiexposure)
+    assert result.meta.cal_step.combine_1d == "SKIPPED"
+    watcher2.assert_seen()
diff --git a/jwst/pipeline/calwebb_spec3.py b/jwst/pipeline/calwebb_spec3.py
index c7cec820d6..ed09baff6d 100644
--- a/jwst/pipeline/calwebb_spec3.py
+++ b/jwst/pipeline/calwebb_spec3.py
@@ -296,13 +296,17 @@ def process(self, input_data):
                     extraction_complete = (
                         result is not None and result.meta.cal_step.extract_1d == "COMPLETE"
                     )
-                    if extraction_complete:
-                        # Combine the results for all sources
-                        comb = self.combine_1d.run(result)
-                        # add metadata that only WFSS wants
-                        comb.spec[0].source_ra = result.spec[0].spec_table["SOURCE_RA"][0]
-                        comb.spec[0].source_dec = result.spec[0].spec_table["SOURCE_DEC"][0]
-                        wfss_comb.append(comb)
+                    if not extraction_complete:
+                        continue
+                    # Combine the results for all sources
+                    comb = self.combine_1d.run(result)
+                    comb_complete = comb is not None and comb.meta.cal_step.combine_1d == "COMPLETE"
+                    if not comb_complete:
+                        continue
+                    # add metadata that only WFSS wants
+                    comb.spec[0].source_ra = result.spec[0].spec_table["SOURCE_RA"][0]
+                    comb.spec[0].source_dec = result.spec[0].spec_table["SOURCE_DEC"][0]
+                    wfss_comb.append(comb)
 
             elif resample_complete is not None and resample_complete.upper() == "COMPLETE":
                 # If 2D data were resampled and combined, just do a 1D extraction