jQuery functions not responding after append()

I'm creating a series of div boxes that lets users add/remove items from each box with jQuery. I find that after I add a new element to a box, the click function I have bound to that element will not respond. Here's roughly what my code looks like:

$(".add").click(function() {
$("#targetbox").append("<span class='remove'>This element was added</span>");
});

$(".remove").click(function() {
alert("removing");
$(this).remove();
});

If I pre-populate #targetbox with items, they respond to the click function. It's only the items that are dynamically added that do not respond to the function.