In this talk I will describe an approach to Serre functors for blocks of the category O based on Harish-Chandra bimodules. The advanatage of this approach is that it extends to the case of Lie superalgebras. As an  application we obtain that the algebras describing finite-dimensional q(2n)-supermodules are symmetric (in the case of q(2n-1) it is obviously not, in general). The cases of q(1) and q(2) will be treated in detailes. The talk is based on a joint work with Vanessa Miemietz.