diff --git a/src/XrdCl/XrdClTaskManager.cc b/src/XrdCl/XrdClTaskManager.cc
index a3e0c5ce725..aa16cc0f706 100644
--- a/src/XrdCl/XrdClTaskManager.cc
+++ b/src/XrdCl/XrdClTaskManager.cc
@@ -21,6 +21,7 @@
 #include "XrdCl/XrdClUtils.hh"
 #include "XrdCl/XrdClDefaultEnv.hh"
 #include "XrdCl/XrdClConstants.hh"
+#include "XrdSys/XrdSysTimer.hh"
 
 #include <iostream>
 
@@ -240,7 +241,7 @@ namespace XrdCl
       // Enable the cancelation and go to sleep
       //------------------------------------------------------------------------
       pthread_setcancelstate( PTHREAD_CANCEL_ENABLE, 0 );
-      ::sleep( pResolution );
+      XrdSysTimer::Wait( pResolution*1000 );
     }
   }
 }
diff --git a/src/XrdCl/XrdClThirdPartyCopyJob.cc b/src/XrdCl/XrdClThirdPartyCopyJob.cc
index 43ac1a8f66a..4150c2af8ca 100644
--- a/src/XrdCl/XrdClThirdPartyCopyJob.cc
+++ b/src/XrdCl/XrdClThirdPartyCopyJob.cc
@@ -26,6 +26,7 @@
 #include "XrdCl/XrdClMonitor.hh"
 #include "XrdOuc/XrdOucTPC.hh"
 #include "XrdSys/XrdSysPthread.hh"
+#include "XrdSys/XrdSysTimer.hh"
 #include <iostream>
 #include <cctype>
 #include <sstream>
@@ -243,7 +244,7 @@ namespace XrdCl
     //--------------------------------------------------------------------------
     while( 1 )
     {
-      sleep(1);
+      XrdSysTimer::Wait( 1000 );
 
       if( progress )
       {