  We present the first simultaneous trapping of two different ultracold atomic
species in a conservative trap. Lithium and cesium atoms are stored in an
optical dipole trap formed by the focus of a CO$_2$ laser. Techniques for
loading both species of atoms are discussed and observations of elastic and
inelastic collisions between the two species are presented. A model for
sympathetic cooling of two species with strongly different mass in the presence
of slow evaporation is developed. From the observed Cs-induced evaporation of
Li atoms we estimate a cross section for cold elastic Li-Cs collisions.
