One-photon laser excitation of Xe(6s[3/2](2)) and Kr(5s[3/2](2)) atoms that were generated in a discharge-flow reactor was used to study the collisional relaxation of the Kr(5p’[3/2](1), [3/2](2), and [1/2](1)), the Xe(7p[3/2](2), [3/2](1), [5/2](2), and [5/2](3)), and the Xe(6p’[3/2](1), [3/2](2), and [1/2](1)) states in He and Ar. Both cw and pulsed laser excitation techniques were utilized to obtain the total deactivation rate constants and product formation rate constants at 300 K. Collisions with He mainly produce Xe* and Kr* product states with small energy defects, but the rate constants can be as large as 20X10(-10) cm(3) atom(-1) s(-1) which correspond to thermally averaged cross sections of 150 Angstrom(2). Because of the rapid collisional coupling of populations in nearly isoenergetic levels, multicomponent exponential decay of the initially produced state is frequently observed. The deactivation rate constants for Ar are smaller than for He, but the product distributions tend to be more diverse than for He, and arguments based only on energy defects are riot necessarily a good guide to the favored product state(s) from Ar collisions. The magnitude of the quenching cross sections for Ar is consistent with the crossing of an entrance channel with several diabatic exit channel potentials. However, the superlarge quenching cross sections for Xe*-He to just one or two product levels require special considerations. The Kr(5p’) and Xe(6p’ and 7p) rate constants with He are discussed with respect to collisional effects upon the use of cw optical pumping to convert populations in the metastable Xe(6s[3/2](2)) and Kr(5s[3/2](2)) levels to the Xe(6s’[1/2](0)) and Kr(5s’[1/2](0)) levels.