We calculate the cross sections for the p(p, nπ + )p and p(p, pπ 0 )p reactions for proton beam energies near threshold in a covariant one-bosonexchange model, which incorporates the exchange of π, ρ, σ and ω mesons and treats both nucleon and delta isobar as intermediate states. The final state interaction effects have also been included. The ω meson exchange is found to contribute significantly at these energies, which, along with other meson exchanges, provides an excellent agreement with the data. The cross sections at beam energies ≤ 300 MeV are almost free from the contributions of the ∆ isobar excitation.KEYWORD: π 0 and π + production near threshold, covariant oneboson-exchange model, contribution of heavy meson exchange.