来源：http://www.delphitricks.com/source-code/windows/check_if_a_process_is_running.html

uses TlHelp32; 
    function processExists(exeFileName: string): Boolean; 
var 
  ContinueLoop: BOOL; 
  FSnapshotHandle: THandle; 
  FProcessEntry32: TProcessEntry32; 
begin 
  FSnapshotHandle := CreateToolhelp32Snapshot(TH32CS_SNAPPROCESS, 0); 
  FProcessEntry32.dwSize := SizeOf(FProcessEntry32); 
  ContinueLoop := Process32First(FSnapshotHandle, FProcessEntry32); 
  Result := False; 
  while Integer(ContinueLoop) <> 0 do 
  begin 
    if ((UpperCase(ExtractFileName(FProcessEntry32.szExeFile)) = 
      UpperCase(ExeFileName)) or (UpperCase(FProcessEntry32.szExeFile) = 
      UpperCase(ExeFileName))) then 
    begin 
      Result := True; 
    end; 
    ContinueLoop := Process32Next(FSnapshotHandle, FProcessEntry32); 
  end; 
  CloseHandle(FSnapshotHandle); 
end; 
procedure TForm1.Button1Click(Sender: TObject); 
begin 
  if processExists('notepad.exe') then 
    ShowMessage('process is running') 
  else 
    ShowMessage('process not running'); 
end;

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如果您正在编写一些自动更新代码，您还可以考虑与应用程序建立某种连接，并告诉它自行关闭。
例如，这可能涉及到在应用程序的主窗口发布一条消息，告诉它关闭自己。或者打开一个IPC管道等。

uses TlHelp32, PsAPI;
function ProcessExists(anExeFileName: string): Boolean;
var
  ContinueLoop: BOOL;
  FSnapshotHandle: THandle;
  FProcessEntry32: TProcessEntry32;
  fullPath: string;
  myHandle: THandle;
  myPID: DWORD;
begin
  // wsyma 2016-04-20 Erkennung, ob ein Prozess in einem bestimmten Pfad schon gestartet wurde.
  // Detection wether a process in a certain path is allready started.
  // http://stackoverflow.com/questions/876224/how-to-check-if-a-process-is-running-using-delphi
  // http://swissdelphicenter.ch/en/showcode.php?id=2010
  FSnapshotHandle := CreateToolhelp32Snapshot(TH32CS_SNAPPROCESS, 0);
  FProcessEntry32.dwSize := SizeOf(FProcessEntry32);
  ContinueLoop := Process32First(FSnapshotHandle, FProcessEntry32);
  Result := False;
  while Integer(ContinueLoop) <> 0 do
  begin
    if UpperCase(ExtractFileName(FProcessEntry32.szExeFile)) = UpperCase(ExtractFileName(anExeFileName)) then
    begin
      myPID := FProcessEntry32.th32ProcessID;
      myHandle := OpenProcess(PROCESS_QUERY_INFORMATION or PROCESS_VM_READ, False, myPID);
      if myHandle <> 0 then
      try
        SetLength(fullPath, MAX_PATH);
        if GetModuleFileNameEx(myHandle, 0, PChar(fullPath), MAX_PATH) > 0 then
        begin
          SetLength(fullPath, StrLen(PChar(fullPath)));
          if UpperCase(fullPath) = UpperCase(anExeFileName) then
            Result := True;
        end else
          fullPath := '';
      finally
        CloseHandle(myHandle);
      end;
      if Result then
        Break;
    end;
    ContinueLoop := Process32Next(FSnapshotHandle, FProcessEntry32);
  end;
  CloseHandle(FSnapshotHandle);
end;

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如果你可以控制应用程序（正如你的问题所暗示的那样），一个很好的方法是在进程开始的早期创建一个命名的文件Map对象。这类似于从RedLEON创建一个互斥体的建议。

// Add this into the application you wish to update
CreateFileMapping(HWND($FFFFFFFF), nil, PAGE_READONLY, 0, 32, 'MAIN-PROGRAM');
// Note: Mapping object is destroyed when your application exits
// Add this into your updater application       
var
    hMapping: HWND;
begin
    hMapping := CreateFileMapping(HWND($FFFFFFFF), nil, PAGE_READONLY, 0, 32, 'MAIN-PROGRAM');
    if (hMapping <> 0) then
        begin
        if (GetLastError() = ERROR_ALREADY_EXISTS) then
            ShowMessage('Application to update is already running!');
        end;

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查看MSDN documentation on CreateFileMapping以了解更多详细信息。
另请参阅this question的公认答案，其中涵盖了路加的答案并提供了其他解决方案。

我正在输入这些代码初始化主机的一部分。

initialization
mHandle := CreateMutex(nil, True, 'myApp.ts');
if GetLastError = ERROR_ALREADY_EXISTS then
begin
  MessageDlg('Program already running!', mtError, [mbOK], 0);
  Halt;
end;

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