  The superconducting properties of a layered system are analyzed for the cases
of zero- and non-zero angular momentum of the pairs. The effective
thermodynamic potential for the quasi-2D XY-model for the gradients of the
phase of the order parameter is derived from the microscopic superconducting
Hamiltonian. The dependence of the superconducting critical temperature T_c on
doping, or carrier density, is studied at different values of coupling and
inter-layer hopping. It is shown that the critical temperature T_c of the
layered system can be lower than the critical temperature of the
two-dimensional Berezinskii-Kosterlitz-Thouless transition T_BKT at some values
of the model parameters, contrary to the case when the parameters of the
XY-model do not depend on the microscopic Hamiltonian parameters.
