The cross sections for the collisional deexcitation of neon atoms in the lowest excited P-1(1) state by Ar, Kr, Xe, N-2, O-2, CO, NO, and CH4, and in the lowest excited P-3(1) state by O-2 and CH4 have been measured at a mean collisional energy corresponding to room temperature. Data are also included for collisions of argon atoms in the lowest excited P-1(1) and P-3(1) states by C2H4, cyclo-C3H6, and C3H8, and collisions of krypton atoms in the lowest excited P-1(1) and P-3(1) states by C2H4 and cyclo-C3H6. The measured cross sections, together with those obtained in our previous studies, are compared with the cross sections calculated using the Watanabe-Katsuura theory. An extension of the Watanabe-Katsuura theory to the deexcitation of excited rare gas atoms in collisions with molecular quenchers, not atoms, is examined. (C) 2003 American Institute of Physics.