  We study the mechanism of the associated Lambda-kaon and Sigma-kaon
production in nucleon-nucleon collisions over an extended range of near
threshold beam energies within an effective Lagrangian model, to understand of
the new data on pp --> p Lambda K+ and pp --> p Sigma0 K+ reactions published
recently by the COSY-11 collaboration. In this theory, the hyperon production
proceeds via the excitation of N*(1650), N*(1710), and N*(1720) baryonic
resonances. Interplay of the relative contributions of various resonances to
the cross sections, is discussed as a function of the beam energy over a larger
near threshold energy domain. Predictions of our model are given for the total
cross sections of pp --> p Sigma+K0, pp --> n Sigma+K+, and pn --> n Lambda K+
reactions.
