How do i put two accordions on one page?

Hi,
How can I have two accordions on the same page? I have tried the using
two different classes but that doesn't work.
$(function() {
        $("#accordion").accordion();
        $("#accordion1").accordion();
    });
Using the same class for both accordions causes only the first
accordion to be rendered but not the last one in the page.
Any help is greatly appreciated.
Thanks,
Peter.