In this paper we investigate the influence of decoherence effects on quantum states generated as a result of the cross-Kerr nonlinear interaction between two modes. For Markovian losses (both photon loss and dephasing), a region of parameters when losses still do not lead to destruction of nonclassicality is identified. We emphasize the difference in impact of losses in the process of state generation as opposed to those occurring in propagation channel. We show, moreover, that correlated losses in modern realizations of schemes of large cross-Kerr nonlinearity might lead to enhancement of nonclassicality.795