diff --git a/python/src/com/jetbrains/python/inspections/PyArgumentListInspection.java b/python/src/com/jetbrains/python/inspections/PyArgumentListInspection.java
index 467fdcab9b10..b07f695c0e07 100644
--- a/python/src/com/jetbrains/python/inspections/PyArgumentListInspection.java
+++ b/python/src/com/jetbrains/python/inspections/PyArgumentListInspection.java
@@ -8,6 +8,7 @@ import com.intellij.codeInspection.ProblemHighlightType;
 import com.intellij.codeInspection.ProblemsHolder;
 import com.intellij.lang.ASTNode;
 import com.intellij.openapi.project.Project;
+import com.intellij.openapi.util.Conditions;
 import com.intellij.psi.PsiElementVisitor;
 import com.intellij.psi.PsiPolyVariantReference;
 import com.intellij.psi.ResolveResult;
@@ -86,7 +87,9 @@ public class PyArgumentListInspection extends PyInspection {
           else { // possible unfilled params
             for (int i = firstParamOffset; i < params.size(); i++) {
               final PyCallableParameter parameter = params.get(i);
-              if (parameter.getParameter() instanceof PySingleStarParameter) continue;
+              if (parameter.getParameter() instanceof PySingleStarParameter || parameter.getParameter() instanceof PySlashParameter) {
+                continue;
+              }
               // param tuples, non-starred or non-default won't do
               if (!parameter.isKeywordContainer() && !parameter.isPositionalContainer() && !parameter.hasDefaultValue()) {
                 final String parameterName = parameter.getName();
diff --git a/python/src/com/jetbrains/python/psi/impl/PyCallExpressionHelper.java b/python/src/com/jetbrains/python/psi/impl/PyCallExpressionHelper.java
index b27da4d605b7..569436edf529 100644
--- a/python/src/com/jetbrains/python/psi/impl/PyCallExpressionHelper.java
+++ b/python/src/com/jetbrains/python/psi/impl/PyCallExpressionHelper.java
@@ -859,6 +859,7 @@ public class PyCallExpressionHelper {
   @NotNull
   private static ArgumentMappingResults analyzeArguments(@NotNull List<PyExpression> arguments,
                                                          @NotNull List<PyCallableParameter> parameters) {
+    boolean positionalOnlyMode = ContainerUtil.exists(parameters, p -> p.getParameter() instanceof PySlashParameter);
     boolean seenSingleStar = false;
     boolean mappedVariadicArgumentsToParameters = false;
     final Map<PyExpression, PyCallableParameter> mappedParameters = new LinkedHashMap<>();
@@ -920,7 +921,17 @@ public class PyCallExpressionHelper {
           }
         }
         else {
-          if (allPositionalArguments.isEmpty()) {
+          if (positionalOnlyMode) {
+            final PyExpression positionalArgument = next(allPositionalArguments);
+
+            if (positionalArgument != null) {
+              mappedParameters.put(positionalArgument, parameter);
+            }
+            else if (!parameter.hasDefaultValue()) {
+              unmappedParameters.add(parameter);
+            }
+          }
+          else if (allPositionalArguments.isEmpty()) {
             final PyKeywordArgument keywordArgument = removeKeywordArgument(keywordArguments, parameterName);
             if (keywordArgument != null) {
               mappedParameters.put(keywordArgument, parameter);
@@ -970,6 +981,9 @@ public class PyCallExpressionHelper {
           mappedVariadicArgumentsToParameters = true;
         }
       }
+      else if (psi instanceof PySlashParameter) {
+        positionalOnlyMode = false;
+      }
       else if (psi instanceof PySingleStarParameter) {
         seenSingleStar = true;
       }
@@ -1285,15 +1299,6 @@ public class PyCallExpressionHelper {
     return list.isEmpty() ? null : list.remove(0);
   }
 
-  @NotNull
-  private static List<PyCallableParameter> dropImplicitParameters(@NotNull List<PyCallableParameter> parameters, int offset) {
-    final ArrayList<PyCallableParameter> results = new ArrayList<>(parameters);
-    for (int i = 0; i < offset && !results.isEmpty(); i++) {
-      results.remove(0);
-    }
-    return results;
-  }
-
   @NotNull
   private static List<PyCallableParameter> filterExplicitParameters(@NotNull List<PyCallableParameter> parameters,
                                                                     @Nullable PyCallable callable,
diff --git a/python/testData/inspections/PyArgumentListInspection/positionalOnlyParameters.py b/python/testData/inspections/PyArgumentListInspection/positionalOnlyParameters.py
new file mode 100644
index 000000000000..09a0c948f1cf
--- /dev/null
+++ b/python/testData/inspections/PyArgumentListInspection/positionalOnlyParameters.py
@@ -0,0 +1,81 @@
+def foo(a, /, b, *args, c, **kwargs):
+    print(a, b, args, c, kwargs)
+
+# valid
+# b as positional
+foo(1, 2, c=3)
+foo(1, 2, 3, c=3)
+foo(1, 2, 3, c=3, d=4)
+
+# b as keyword
+foo(1, b=2, c=3)
+foo(1, c=3, b=2)
+
+# invalid
+foo(<warning descr="Parameter 'a' unfilled"><warning descr="Parameter 'b' unfilled"><warning descr="Parameter 'c' unfilled">)</warning></warning></warning>
+foo(c=3<warning descr="Parameter 'a' unfilled"><warning descr="Parameter 'b' unfilled">)</warning></warning>
+foo(b=2, c=3<warning descr="Parameter 'a' unfilled">)</warning>
+foo(a=1, b=2, c=3<warning descr="Parameter 'a' unfilled">)</warning>
+
+
+def foo2(a, /, b=2, *args, c, **kwargs):
+    print(a, b, args, c, kwargs)
+
+# valid
+# b as positional
+foo2(1, 2, c=3)
+foo2(1, 2, 3, c=3)
+foo2(1, 2, 3, c=3, d=4)
+
+# b as keyword
+foo2(1, b=2, c=3)
+foo2(1, c=3, b=2)
+
+# no b
+foo2(1, c=3)
+
+# invalid
+foo2(<warning descr="Parameter 'a' unfilled"><warning descr="Parameter 'c' unfilled">)</warning></warning>
+foo2(c=3<warning descr="Parameter 'a' unfilled">)</warning>
+foo2(b=2, c=3<warning descr="Parameter 'a' unfilled">)</warning>
+foo2(a=1, b=2, c=3<warning descr="Parameter 'a' unfilled">)</warning>
+
+
+def foo3(a=1, /, b=2, *args, c, **kwargs):
+    print(a, b, args, c, kwargs)
+
+# valid
+# b as positional
+foo3(1, 2, c=3)
+foo3(1, 2, 3, c=3)
+foo3(1, 2, 3, c=3, d=4)
+
+# b as keyword
+foo3(1, b=2, c=3)
+foo3(1, c=3, b=2)
+
+# no b
+foo3(1, c=3)
+
+# no a, b as positional
+foo3(2, c=3)
+foo3(2, 3, c=3)
+foo3(2, 3, c=3, d=4)
+
+# no a, b as keyword
+foo3(b=2, c=3)
+foo3(c=3, b=2)
+
+# no a, no b
+foo3(c=3)
+foo3(a=1, b=2, c=3)  # a goes to kwargs
+
+# invalid
+foo3(<warning descr="Parameter 'c' unfilled">)</warning>
+
+
+def foo4(a=1, /, b=2, *args, c):
+    print(a, b, args, c)
+
+# invalid
+foo4(<warning descr="Unexpected argument">a=1</warning>, b=2, c=3)
diff --git a/python/testSrc/com/jetbrains/python/inspections/PyArgumentListInspectionTest.java b/python/testSrc/com/jetbrains/python/inspections/PyArgumentListInspectionTest.java
index 3a57aa1462fe..744121a1e7c5 100644
--- a/python/testSrc/com/jetbrains/python/inspections/PyArgumentListInspectionTest.java
+++ b/python/testSrc/com/jetbrains/python/inspections/PyArgumentListInspectionTest.java
@@ -376,4 +376,9 @@ public class PyArgumentListInspectionTest extends PyInspectionTestCase {
   public void testAnotherMethodIsWrappedIntoStatic() {
     doMultiFileTest();
   }
+
+  // PY-35512
+  public void testPositionalOnlyParameters() {
+    runWithLanguageLevel(LanguageLevel.PYTHON38, this::doTest);
+  }
 }