  We investigate the associated strangeness Lambda K+ and Sigma0 K+ productions
in proton-proton collisions within an effective Lagrangian model. The initial
interaction between the two nucleons is modeled by the exchange of pi, rho,
omega, and sigma mesons and the strangeness production proceeds via excitations
of N*(1650), N*(1710), and N*(1720) baryonic resonances. The parameters of the
model at the nucleon-nucleon-meson vertices are determined by fitting the
elastic nucleon-nucleon scattering with an effective interaction based on the
exchange of these four mesons, while those at the resonance vertices are
calculated from the known decay widths of the resonances and from the vector
meson dominance model. Experimental data taken recently by the COSY-11
collaboration are described well by this approach. The one-pion-exchange
diagram dominates the production process at both higher and lower beam
energies. The excitation of the N*(1650) resonance dominates both the
production channels at near threshold energies. Our model with final state
interaction effects among the outgoing particles included within the
Watson-Migdal approximation, is able to explain the observed beam energy
dependence of the ratio of the total cross sections of these two reactions.
