Multiple cycles (movie clips) can be used in conjunction with one another. Characters have their own cycles, as do environments.

Examples:
Old Popeye

Class Assignment: Flock of Seagulls (not the 80's band)
Here's a tutorial that covers lots of ground at Creative Cow.
Part 1
Part 2

Some important concepts are the notions of looping and staggering loops within a composition, then nesting compositions into others.