diff --git a/R/expect-inheritance.R b/R/expect-inheritance.R
index 58dd72b84..3238fcdc7 100644
--- a/R/expect-inheritance.R
+++ b/R/expect-inheritance.R
@@ -20,16 +20,17 @@
 #' See [expect_vector()] for testing properties of objects created by vctrs.
 #'
 #' @param type String giving base type (as returned by [typeof()]).
-#' @param class
-#'  * `expect_type()`: a single string giving an R base type.
-#'  * `expect_s3_class()`: a character vector of class names or `NA` to assert
-#'    that `object` isn't an S3 object. If you provide multiple class names,
-#'    the test will pass if `object` inherits from any of them, unless
-#'    `exact = TRUE`.
-#'  * `expect_s4_class()`: a character vector of class names or `NA` to assert
-#'    that `object` isn't an S4 object.
-#'  * `expect_r6_class()`: a string.
-#'  * `expect_s7_class()`: an [S7::S7_class()] object.
+#' @param class The required type varies depending on the function:
+#'   * `expect_type()`: a string.
+#'   * `expect_s3_class()`: a string or character vector. The behaviour of
+#'     multiple values (i.e. a character vector) is controlled by the
+#'     `exact` argument.
+#'   * `expect_s4_class()`: a string.
+#'   * `expect_r6_class()`: a string.
+#'   * `expect_s7_class()`: an [S7::S7_class()] object.
+#'
+#'   For historical reasons, `expect_s3_class()` and `expect_s4_class()` also
+#'   take `NA` to assert that the `object` is not an S3 or S4 object.
 #' @inheritParams expect_that
 #' @family expectations
 #' @examples
@@ -85,7 +86,7 @@ expect_type <- function(object, type) {
 #' @rdname inheritance-expectations
 #' @param exact If `FALSE`, the default, checks that `object` inherits
 #'   from any element of `class`. If `TRUE`, checks that object has a class
-#'   that's identical to `class`.
+#'   that exactly matches `class`.
 expect_s3_class <- function(object, class, exact = FALSE) {
   check_bool(exact)
 
diff --git a/man/inheritance-expectations.Rd b/man/inheritance-expectations.Rd
index 5d678b9d9..41ae792de 100644
--- a/man/inheritance-expectations.Rd
+++ b/man/inheritance-expectations.Rd
@@ -28,21 +28,23 @@ within a function or for loop. See \link{quasi_label} for more details.}
 
 \item{type}{String giving base type (as returned by \code{\link[=typeof]{typeof()}}).}
 
-\item{class}{\itemize{
-\item \code{expect_type()}: a single string giving an R base type.
-\item \code{expect_s3_class()}: a character vector of class names or \code{NA} to assert
-that \code{object} isn't an S3 object. If you provide multiple class names,
-the test will pass if \code{object} inherits from any of them, unless
-\code{exact = TRUE}.
-\item \code{expect_s4_class()}: a character vector of class names or \code{NA} to assert
-that \code{object} isn't an S4 object.
+\item{class}{The required type varies depending on the function:
+\itemize{
+\item \code{expect_type()}: a string.
+\item \code{expect_s3_class()}: a string or character vector. The behaviour of
+multiple values (i.e. a character vector) is controlled by the
+\code{exact} argument.
+\item \code{expect_s4_class()}: a string.
 \item \code{expect_r6_class()}: a string.
 \item \code{expect_s7_class()}: an \code{\link[S7:S7_class]{S7::S7_class()}} object.
-}}
+}
+
+For historical reasons, \code{expect_s3_class()} and \code{expect_s4_class()} also
+take \code{NA} to assert that the \code{object} is not an S3 or S4 object.}
 
 \item{exact}{If \code{FALSE}, the default, checks that \code{object} inherits
 from any element of \code{class}. If \code{TRUE}, checks that object has a class
-that's identical to \code{class}.}
+that exactly matches \code{class}.}
 }
 \description{
 See \url{https://adv-r.hadley.nz/oo.html} for an overview of R's OO systems, and