diff --git a/R/check_heteroscedasticity.R b/R/check_heteroscedasticity.R
index f3e0368c2..526f2f184 100644
--- a/R/check_heteroscedasticity.R
+++ b/R/check_heteroscedasticity.R
@@ -41,8 +41,14 @@ check_heteroskedasticity <- check_heteroscedasticity
 #' @export
 check_heteroscedasticity.default <- function(x, ...) {
   # only for linear models
-  if (!insight::model_info(x)$is_linear) {
-    stop("This Breusch-Pagan Test currently only works Gaussian models.")
+  info <- insight::model_info(x)
+  if (!info$is_linear) {
+    msg <- "This Breusch-Pagan Test currently only works Gaussian models."
+    if (info$is_count) {
+      paste0(msg, " You may check your model for overdispersion or zero-inflation instead (see 'check_overdispersion()' and 'check_zeroinflation()').")
+    }
+    message(msg)
+    return(NULL)
   }
 
   r <- .pearson_residuals(x)
diff --git a/R/check_normality.R b/R/check_normality.R
index c42204e25..acd2806b1 100644
--- a/R/check_normality.R
+++ b/R/check_normality.R
@@ -47,8 +47,15 @@ check_normality <- function(x, ...) {
 }
 
 
+#' @importFrom insight model_info
 #' @export
 check_normality.default <- function(x, ...) {
+  # valid model?
+  if (!insight::model_info(x)$is_linear) {
+    message("Checking normality of residuals is only useful an appropriate assumption for linear models.")
+    return(NULL)
+  }
+
   # check for normality of residuals
   p.val <- .check_normality(stats::rstandard(x), x)
 
@@ -73,6 +80,12 @@ check_normality.merMod <- function(x, effects = c("fixed", "random"), ...) {
   effects <- match.arg(effects)
   info <- insight::model_info(x)
 
+  # valid model?
+  if (!info$is_linear) {
+    message("Checking normality of residuals is only useful an appropriate assumption for linear models.")
+    return(NULL)
+  }
+
   if (effects == "random") {
     if (!requireNamespace("lme4", quietly = TRUE)) {
       stop("Package 'lme4' required for this function to work. Please install it.", call. = FALSE)