Overpartition pairs have recently played a key role in
combinatorial studies of
q-series identities, including families of
idenities of the Rogers-Ramanujan type.
An important statistic for overpartition pairs is the rank, which is a
generalization
of Dyson's classical rank of a partition. In this talk we
investigate the role that this
generalized rank plays in congruence properties for the number of
overpartition
pairs of n.