  Let V be a vertex operator algebra. We construct a sequence of associative
algebras A_n(V) (n=0,1,2,...) such that A_{n}(V) is a quotient of A_{n+1}(V)
and a pair of functors between the category of A_n(V)-modules which are not
A_{n-1}(V)-modules and the category of admissible V-modules. These functors
exhibit a bijection between the simple modules in each category. We also show
that V is rational if and only if all A_n(V) are finite-dimensional semisimple
algebras.
