How do I add a new class to an element dynamically?

Is there any way to add a new CSS class to an element on :hover?

Like for jQuery, but translated into CSS:

$(element).addClass('someclass');

Short answer no :)

But you could just use the same CSS for the hover like so:

a:hover, .hoverclass {
    background:red;
}

Maybe if you explain why you need the class added, there may be a better solution?