Try:
Process p1 = new Process();
p1.StartInfo.FileName = @"D:\Temp\MyFirstExe";
p1.StartInfo.Arguments = "MyFileName.txt -o myOutputFile.txt";
p1.Start();
Process p2 = new Process();
p2.StartInfo.FileName = @"D:\Temp\MySecondExe";
p2.StartInfo.Arguments = "\"Another set of arguments\" \"to pass through\"";
p2.Start();