The space Hp(A) is a
generalization of the Hardy space Hp for functions analytic on an annulus A. This
paper shows that composition operators are bounded operators on Hp(A) and
obtains an upper bound on the norm of the operator. The space H2(A) is given a
Hilbert space structure and those composition operators that are in the
Hilbert-Schmidt class of operators on H2(A) are characterized in terms of integral
properties of the inducing function.