diff --git a/mathics/format/box/formatvalues.py b/mathics/format/box/formatvalues.py
index a52521bd0..262679cc4 100644
--- a/mathics/format/box/formatvalues.py
+++ b/mathics/format/box/formatvalues.py
@@ -25,7 +25,19 @@
     SymbolPlus,
     SymbolTimes,
 )
-from mathics.core.systemsymbols import SymbolInputForm, SymbolMinus, SymbolOutputForm
+from mathics.core.systemsymbols import (
+    SymbolInfix,
+    SymbolInputForm,
+    SymbolMinus,
+    SymbolOutputForm,
+    SymbolPostfix,
+    SymbolPrefix,
+)
+
+# Operator forms that display only the elements of their first argument,
+# not the argument itself: in Format[f[x__]] := Infix[f[x], "~"], f[x] must
+# not be formatted again.
+OPERATOR_FORMS = (SymbolInfix, SymbolPostfix, SymbolPrefix)
 
 # These Strings are used in Boxing output
 StringElipsis = String("...")
@@ -134,12 +146,25 @@ def format_expr(expr):
             and isinstance(expr, Expression)
             and head not in (SymbolGraphics, SymbolGraphics3D)
         ):
+
+            def format_element(element):
+                return _element_formatters.get(type(element), do_format_element)(
+                    element, evaluation, form
+                )
+
             new_elements = tuple(
                 (
-                    _element_formatters.get(type(element), do_format_element)(
-                        element, evaluation, form
+                    (
+                        to_expression_with_specialization(
+                            element.head,
+                            *(format_element(e) for e in element.elements),
+                        )
+                        if index == 0
+                        and head in OPERATOR_FORMS
+                        and isinstance(element, Expression)
+                        else format_element(element)
                     )
-                    for element in expr.elements
+                    for index, element in enumerate(expr.elements)
                 )
             )
             expr_head = expr.head
diff --git a/test/format/test_format.py b/test/format/test_format.py
index 1d4e05b22..335f6eea5 100644
--- a/test/format/test_format.py
+++ b/test/format/test_format.py
@@ -268,6 +268,33 @@ def test_format_private_doctests(str_expr, str_expected, msg):
             None,
         ),
         ("r[1]", None, "ab", None),
+        # Infix, Prefix and Postfix display the elements of their first
+        # argument, so a format may wrap the expression it formats.
+        (
+            'Format[pInfix[t__]] := Infix[pInfix[t], "~"]; pInfix[a, b]',
+            (),
+            "a ~ b",
+            "Infix of the formatted expression itself",
+        ),
+        ("pInfix[a, pInfix[b, c]] + 1", (), "1 + a ~ b ~ c", "Nested, inside Plus"),
+        (
+            'Format[pLeft[t__]] := Infix[pLeft[t], "~", 300, Left]; pLeft[pLeft[a, b], c]',
+            (),
+            "a ~ b ~ c",
+            "With precedence and grouping",
+        ),
+        (
+            'Format[pPre[x_]] := Prefix[pPre[x], "!"]; pPre[a]',
+            (),
+            "!a",
+            "Prefix of the formatted expression itself",
+        ),
+        (
+            'Format[pPost[x_]] := Postfix[pPost[x], "!!"]; pPost[a]',
+            (),
+            "a!!",
+            "Postfix of the formatted expression itself",
+        ),
         (None, None, None, None),
     ],
 )