The nucleon-nucleon data are fitted by a boundary condition model interaction determined largely by theoretical forms. One-and two-pion, ρ, ω, and η meson exchange adiabatic local potentials determine the interaction outside r0~12μ-1. Only the two-pion-exchange contribution contains a degree of ambiguity measured by the parameters ξ and λ for the pion ladder and nucleon pair diagrams, respectively. The interaction is determined at r0 by an energy-independent boundary condition for those partial waves sensitive to the short-range interaction. A very good fit to the p-p data and a good fit to the n-p data below 350-MeV nucleon laboratory energy, are obtained, comparable to the best phenomenological fits. The optimum or fixed values of exchange particle masses and coupling constants corresponds to their known physical values, and the λ and ξ parameters optimize in their theoretical range. The value attained by r0 corresponds to that predicted by the theory of the boundary condition model. There remain 19 boundary condition parameters, freely fitted, to which the data are sensitive. These may in principle be related to pion-nucleon amplitudes. Rescattering and φ meson exchange contributions to the potential remain to be investigated, as does the effect of coupling to inelastic channels.