  Two-meson-exchange nucleon-nucleon potentials are derived where either one or
both nucleons contains a pair vertex. Physically, the meson-pair vertices are
meant to describe in an effective way (part of) the effects of heavy-meson
exchange and meson-nucleon resonances. {}From the point of view of ``duality,''
these two kinds of contribution are roughly equivalent. The various
possibilities for meson pairs coupling to the nucleon are inspired by the
chiral-invariant phenomenological Lagrangians that have appeared in the
literature. The coupling constants are fixed using the linear $\sigma$ model.
We show that the inclusion of these two-meson exchanges gives a significant
improvement over a potential model including only the standard one-boson
exchanges.
