  Data on the total cross sections for the pp -> pp eta, pn -> pn eta, and pn
-> d eta reactions and the pp -> pp eta differential cross section near
threshold are analysed in a one-meson-exchange model. After including initial
and final-state nucleon-nucleon distortion, the magnitude and most of the
energy dependence are well reproduced. It is found that the contribution of
rho-exchange is larger than that of pi-exchange. With destructive rho/pi
interference in the pp case, the model explains quantitatively the pp -> pp
eta/pn -> pn eta cross section ratio and the slope of the pp -> pp eta
differential cross section. Such an agreement would be destroyed by any
significant eta-exchange term. The residual energy dependence may be associated
with eta-nucleon rescattering that has not been taken into account. The pn ->
pn eta/pn -> d eta ratio depends weakly upon the nature of the particle
exchanges, being determined primarily by the nucleon-nucleon final state
interactions. The proton analysing power is predicted to remain small in the
low energy region.
