We analyse J/psi-production in nucleon-nucleon collisions near threshold in the framework of a general model-independent formalism, which can be applied to any reaction N+N-->N+N+V-0, where V-0=omega, phi or J/psi. Such reactions show large isotopic effects: a large difference for pp and pn collisions, which is due to the different spin structure of the corresponding matrix elements. The analysis of the spin structure and of the polarization observables is based on symmetry properties of the strong interaction. Using existing experimental data on the different decays of the J/psi meson, we suggest a model for N+N-->N+N+J/psi, based on t channel eta+pi exchanges. We predict polarization phenomena for the n+p-->n+p+J/psi reaction and the ratio of cross sections for np and pp collisions. For the processes eta(pi)+N-->N+J/psi we apply two different approaches: vector meson exchange and local four-particle interaction. In both cases we find larger J/psi production in np collisions than in pp collisions.