Hi,
This occurs when Css is not fully loaded.so i will suggest you to load all the css(plugin) first and then load javascript(plugin).i.e. put css plugin link in the header of Page and put javascript plugin link at the end of page also if you are using Update Panel than refer below code.
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<title></title>
<link href="http://cdn.jsdelivr.net/jcarousel/0.2.8/skins/tango/skin.css" rel="Stylesheet" />
</head>
<body>
<!-- all the page stuff and then below links-->
<script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.8.3/jquery.min.js"></script>
<script type="text/javascript" src="http://cdn.jsdelivr.net/jcarousel/0.2.8/jquery.jcarousel.min.js"></script>
<script type="text/javascript">
$(function () {
$('#mycarousel').jcarousel();
});
var prm = Sys.WebForms.PageRequestManager.getInstance();
if (prm != null) {
prm.add_endRequest(function (sender, e) {
if (sender._postBackSettings.panelsToUpdate != null) {
$('#mycarousel').jcarousel();
}
});
};
</script>
</body>
</html>