[en] We have calculated S-wave pion production in pp -→ ppπ⁰ using a fully covariant OBE model, where a boson B created on one of the incoming protons is converted into a neutral pion on the second. The amplitudes for the conversion process BN -→ π⁰N are taken to be the sum of s, u and t-channel pole terms. The model is consistent with the OBE picture of the NN force and accounts for relativistic effects, energy dependence and nonlocality of hadron interactions. The production rate is found to be dominated by a σ-meson pole in a t-channel. The off-shell properties of the various partial production amplitudes are taken into account explicitly. For vector and scalar mesons, offshellness is contained in the nucleon form factor and has a marginal influence only. A pseudovector coupling for the pseudoscalar particles, as assumed in this work, introduces an extra factor of q to the amplitude. Consequently for theπ andη, each of the s and u nucleon pole terms at q² = -3.3fm^-2 becomes a factor of ∼ 7 higher in comparison with its value on mass shell. To account for the off mass shell behavior of the σ-meson pole term, we have used Adler's consistency conditions and the isospin even Top scattering length to determine the σππ vertex in a rather general form. We have found that the π⁰p → π⁰p conversion amplitude off the mass shell is more than a factor ∼ 15 higher in comparison with its on mass shell value. Consequently, the π exchange contribution to the amplitude for the pp -→ ppπ⁰ reaction dominates the production process and brings the calculated cross section to agree with data. A meson production in NN collisions necessarily involves large momentum transfer and therefore, two-pion exchanges which describe short range interactions should play an important role. In the OBE model such contributions are represented by an effective scalar σ-meson pole term. In χPT, an approach which is generally believed to be an effective theory of QCD at low energies, such contributions result from one loop two-pion diagrams. We have extended the existing χPT calculations taking into account all tree and loop diagrams up to chiral order D=2. With these one loop contributions added, it is found that the calculated cross section agrees very well with data and with predictions of the present OBE model calculations. In analogy with a dominant σ meson pole term in the OBE model, there are substantial contributions from isoscalar-scalar two-pion t-channel exchanges. We conclude that two-pion exchanges play an important role in the dynamics of π⁰ in pp → π⁰pp and by taking these into account the OBE model and χPT approaches reproduce the cross section data