Analog of onmousedown is ontouchstart
Analog of onmousemove - ontouchmove
onmouseup - ontouchend
onmouseout - ?
UPDATE1 I mean that when you touch an element, and without releasing allot finger away from it, is the event that I want to catch
After the Update1 I suggest listening to ontouchend which will be triggered when the touch will leave the bound object. But still there is no exact analog. Do you have a particular case where you need to know if the touch exited?