  We study two types of crank moments and two types of rank moments for
overpartitions. We show that the crank moments and their derivatives, along
with certain linear combinations of the rank moments and their derivatives, can
be written in terms of quasimodular forms. We then use this fact to prove exact
relations involving the moments as well as congruence properties modulo 3, 5,
and 7 for some combinatorial functions which may be expressed in terms of the
second moments. Finally, we establish a congruence modulo 3 involving one such
combinatorial function and the Hurwitz class number H(n).
