  It is shown that there are finitely many perfect powers in an elliptic
divisibility sequence whose first term is divisible by 2 or 3. For Mordell
curves the same conclusion is shown to hold if the first term is greater than
1. Examples of Mordell curves and families of congruent number curves are given
with corresponding elliptic divisibility sequences having no perfect power
terms. The proofs combine primitive divisor results with modular methods for
Diophantine equations.
