1) Does API class inherit QObject? If yes, it would be better to create signal in it. fro example, timeCahnged(double), and your code will like this:

Qt Code: 
  1. myClass::myClass()
  2. {
  3.     myapi = new API;
  4.     mylabel = new QLabel;
  5.     connect (myapi, SIGNAL ( timeCahnged(double) ), mylabel, SLOT (setNum(double) ) );
  6. }
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2) Set value by QTimer

Qt Code: 
  1. myClass::myClass()
  2. {
  3.     myapi = new API;
  4.     mylabel = new QLabel;
  5.  
  6.     timer = new QTimer(this);
  7.     connect(timer, SIGNAL(timeout()), this, SLOT(update()));
  8. }
  9.  
  10. int myClass::runapi()
  11. {
  12.     // init API
  13.  
  14.     timer->start(1000);
  15. }
  16.  
  17. void myClass::update ()
  18. {
  19.     mylabel->setNum(myapi->mymethodelapsedtime());
  20. }
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