Storing and cooling simultaneously lithium and sodium atoms in a two-species magneto-optical trap, rate coefficients for collisions between these two atomic species were determined. The experiments were performed at different trap depths, thus for Li atoms the trap losses due to finestructure changing collisions could be distinguished from losses due to radiative escape. The rate coefficient for collisions between sodium and lithium atoms shows also a step when increasing the trap depth. The formation of cold heteronuclear molecules is claimed.