  Cold inelastic collisions between confined cesium (Cs) atoms and Cs$\_2$
molecules are investigated inside a CO$\_2$ laser dipole trap. Inelastic
atom-molecule collisions can be observed and measured with a rate coefficient
of $\sim 2.5 \times 10^{-11} $cm$^3$ s$^{-1}$, mainly independent of the
molecular ro-vibrational state populated. Lifetimes of purely atomic and
molecular samples are essentially limited by rest gas collisions. The pure
molecular trap lifetime ranges 0,3-1 s, four times smaller than the atomic one,
as is also observed in a pure magnetic trap. We give an estimation of the
inelastic molecule-molecule collision rate to be $\sim 10^{-11}$ cm$^{3}$
s$^{-1}$.
