Vi ringrazio moltissimo dell' aiuto !!!
Grazie a Voi ho risolto il problema in questo maniera funzionante:

<html>

<head>
<script>
function checkvalue() {
if (document.getElementById('des1').value!='' && document.getElementById('des2').value=='') {
document.FrontPage_Form2.des2.value=new Date(); }
else if (document.getElementById('des3').value!='' && document.getElementById('des4').value=='') {
document.FrontPage_Form2.des4.value=new Date(); }
}
</script>
</head>

<body>
<form name="FrontPage_Form2" method="POST" action="test4.asp">


<input name="des1" id="des1" size="20" onchange="checkvalue()">
<input name="des2" id="des2" size="20" readonly="true">


<input name="des3" id="des3" size="20" onchange="checkvalue()">
<input name="des4" id="des4" size="20" readonly="true">



</form>

</body>
</html>