  A relativistic covariant one boson exchange model, previously applied to
describe elastic nucleon-nucleon scattering, is extended to study $\eta$
production in NN collisions. The transition amplitude for the elementary
BN->$\eta$N process with B being the meson exchanged (B=$\pi$, $|sigma$,$\eta$,
$\rho$, $\omega$ and $\delta$) are taken to be the sum of four terms
corresponding to s and u-channels with a nucleon or a nucleon isobar
N*(1535MeV) in the intermediate states. Taking the relative phases of the
various exchange amplitudes to be +1, the model reproduces the cross sections
for the $NN\to X\eta$ reactions in a consistent manner. In the limit where all
$\eta$'s are produced via N^* excitations, interference terms between the
overall contributions from the exchange of pseudoscalart and scalar mesons with
that of vector mesons cancel out. Consequently, much of the ambiguities in the
model predictions due to unknown relative phases of different vector
pseudoscalar exchanges are strongly reduced.
