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We evaluate the threshold matrix-element for the reaction $pp \to pp\pi^0$ ina fully relativistic Feynman diagrammatic approach. We employ a simpleeffective range approximation to take care of the S-wave $pp$ final-stateinteraction. The experimental value for the threshold amplitude ${\cal A} =(2.7 - i 0.3)$ fm$^4$ can be reproduced by contributions from tree level chiral(long-range) pion exchange and short-range effects related to vector mesonexchanges, with $\omega$ exchange giving the largest individual contribution.Pion loop effects appear to be small. We stress that the commonly used heavybaryon formalism is not applicable in the NN-system above the pion productionthreshold due to the large external momentum, $|\vec p | \simeq \sqrt{Mm_\pi}$, with $M$ and $m_\pi$ the nucleon and the pion mass, respectively. Wefurthermore investigate the reaction $pp\to p n \pi^+$ near threshold withinthe same approach. We extract from the data the triplet threshold amplitude as${\cal B}= (2.8 -i 1.5)$ fm$^4$. Its real part can be well understood from(relativistic) tree level meson-exchange diagrams. In addition, we investigatethe process $pp \to pp \eta$ near threshold. We use a simple factorizationansatz for the $pp\eta$ final-state interaction and extract from the data themodulus of the threshold amplitude, $|{\cal C}| = 1.32 $fm$^4$. With $g_{\etaN}=5.3$, this value can be reproduced by (relativistic) tree levelmeson-exchange diagrams and $\eta$-rescattering, whose strength is fixed by the$\eta N$ scattering length. We also comment on the recent near threshold datafor $\eta'$-production.Comment: 28 pp, LaTeX, 9 figs, uses epsf, updated version. To be published in  Eur. Phys. J. A (1999). **Title changed again*

Novel approach to pion and eta production in proton-proton collisions near threshold