diff --git a/tests/testthat/test-delta.R b/tests/testthat/test-delta.R
index e8208fd2c..ed0134c2a 100644
--- a/tests/testthat/test-delta.R
+++ b/tests/testthat/test-delta.R
@@ -223,4 +223,18 @@ test_that("Delta-Gengamma family fits", {
   expect_equal(sr_gengamma$ln_tau_E, sr_dgg$ln_tau_E[2], tolerance = 1e-4)
   expect_equal(sr_gengamma$ln_kappa[1,1], sr_dgg$ln_kappa[1,2], tolerance = 1e-4)
   expect_equal(sr_bin$ln_kappa[1,1], sr_dgg$ln_kappa[1,1], tolerance = 1e-4)
+})
+
+test_that("delta_gengamma() Poisson-link family fits", {
+  skip_on_cran()
+  skip_on_ci()
+
+  fit_pgg <- sdmTMB(density ~ 1,
+    data = pcod, mesh = pcod_spde,
+    spatial = "off",
+    family = delta_gengamma(link1 = 'log', link2 = 'log', type = "poisson-link")
+  )
+  fit_pgg$sd_report
+  s <- as.list(fit_pgg$sd_report, "Std. Error")
+  expect_true(sum(is.na(s$b_j)) == 0L)
 })
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