diff --git a/flang/lib/Semantics/check-acc-structure.cpp b/flang/lib/Semantics/check-acc-structure.cpp
--- a/flang/lib/Semantics/check-acc-structure.cpp
+++ b/flang/lib/Semantics/check-acc-structure.cpp
@@ -5,9 +5,10 @@
 // SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
 //
 //===----------------------------------------------------------------------===//
-
 #include "check-acc-structure.h"
+#include "flang/Common/template.h"
 #include "flang/Parser/parse-tree.h"
+#include "flang/Semantics/symbol.h"
 #include "flang/Semantics/tools.h"
 
 #define CHECK_SIMPLE_CLAUSE(X, Y) \
@@ -45,12 +46,36 @@
     llvm::acc::Clause::ACCC_bind, llvm::acc::Clause::ACCC_gang,
     llvm::acc::Clause::ACCC_vector, llvm::acc::Clause::ACCC_worker};
 
+class ConstructSymbolSet {
+public:
+  template <typename T> bool Pre(const T &) { return true; }
+  template <typename T> void Post(const T &) {}
+  bool Pre(const parser::DoConstruct &doConstruct) {
+    const auto &doStmt{
+        std::get<parser::Statement<parser::NonLabelDoStmt>>(doConstruct.t)};
+    if (const auto *currentLabel{MaybeGetStmtName(doStmt.statement)}) {
+      const Symbol &sym{*currentLabel->symbol};
+      labels_.insert(sym);
+    }
+    return true;
+  }
+  SymbolSet labels() { return labels_; }
+
+private:
+  // Return the (possibly null) name of the statement
+  template <typename A>
+  static const parser::Name *MaybeGetStmtName(const A &a) {
+    return common::GetPtrFromOptional(std::get<0>(a.t));
+  }
+  SymbolSet labels_;
+};
+
 class NoBranchingEnforce {
 public:
-  NoBranchingEnforce(SemanticsContext &context,
+  NoBranchingEnforce(SemanticsContext &context, SymbolSet &&labels,
       parser::CharBlock sourcePosition, llvm::acc::Directive directive)
-      : context_{context}, sourcePosition_{sourcePosition}, currentDirective_{
-                                                                directive} {}
+      : context_{context}, labels_{std::move(labels)},
+        sourcePosition_{sourcePosition}, currentDirective_{directive} {}
   template <typename T> bool Pre(const T &) { return true; }
   template <typename T> void Post(const T &) {}
 
@@ -60,9 +85,15 @@
   }
 
   void Post(const parser::ReturnStmt &) { emitBranchOutError("RETURN"); }
-  void Post(const parser::ExitStmt &) { emitBranchOutError("EXIT"); }
+  void Post(const parser::ExitStmt &exitStmt) {
+    if (const auto *exitLabel{common::GetPtrFromOptional(exitStmt.v)}) {
+      const Symbol &sym{*exitLabel->symbol};
+      if (labels_.find(sym) == labels_.end()) {
+        emitBranchOutError("EXIT");
+      }
+    }
+  }
   void Post(const parser::StopStmt &) { emitBranchOutError("STOP"); }
-
 private:
   parser::MessageFixedText GetEnclosingMsg() {
     return "Enclosing block construct"_en_US;
@@ -78,6 +109,7 @@
   }
 
   SemanticsContext &context_;
+  SymbolSet labels_;
   parser::CharBlock currentStatementSourcePosition_;
   parser::CharBlock sourcePosition_;
   llvm::acc::Directive currentDirective_;
@@ -138,7 +170,12 @@
 void AccStructureChecker::CheckNoBranching(const parser::Block &block,
     const llvm::acc::Directive directive,
     const parser::CharBlock &directiveSource) const {
-  NoBranchingEnforce noBranchingEnforce{context_, directiveSource, directive};
+  // do-construct-name in a do construct is usually called a label.
+  // Works on struct Name and not the Label(R611).
+  ConstructSymbolSet doConstructLabelSet;
+  parser::Walk(block, doConstructLabelSet);
+  NoBranchingEnforce noBranchingEnforce{
+      context_, doConstructLabelSet.labels(), directiveSource, directive};
   parser::Walk(block, noBranchingEnforce);
 }
 
diff --git a/flang/test/Semantics/acc-branch.f90 b/flang/test/Semantics/acc-branch.f90
--- a/flang/test/Semantics/acc-branch.f90
+++ b/flang/test/Semantics/acc-branch.f90
@@ -25,7 +25,6 @@
   do i = 1, N
     a(i) = 3.14
     if(i == N-1) THEN
-      !ERROR: EXIT statement is not allowed in a PARALLEL construct
       exit
     end if
   end do
@@ -54,7 +53,6 @@
   do i = 1, N
     a(i) = 3.14
     if(i == N-1) THEN
-      !ERROR: EXIT statement is not allowed in a KERNELS construct
       exit
     end if
   end do
@@ -82,7 +80,6 @@
   do i = 1, N
     a(i) = 3.14
     if(i == N-1) THEN
-      !ERROR: EXIT statement is not allowed in a SERIAL construct
       exit
     end if
   end do