Recent additions to the list of lunar meteorites include Northwest Africa (NWA) 032 and Dhofar 081. NWA 032 is an unbrecciated basalt, found in Morocco; Dhofar 081 is a fragmented feldspathic breccia, found in Oman. Our goal is the determination of the cosmic ray exposure history of these objects. Most lunar meteorites have complex cosmic ray exposure histories, having been exposed both at some depth on the lunar surface (2{pi} irradiation) before their ejection and as small bodies in space (4{pi} irradiation) during transport from the Moon to the Earth. These exposures were then followed by residence on the Earth's surface, the terrestrial residence time. Unraveling the complex history of these objects requires the measurement of at least four cosmogenic nuclides. The specific goals of these measurements are to constrain the depth of the sample at the time of ejection from the Moon, the transit time from the time of ejection to the time of capture by the Earth, and the residence time on the Earth's surface. These exposure durations in conjunction with the sample depth on the Moon can then be used to model impact and ejection mechanisms. To investigate the complex exposure histories of lunar meteorites, we measured cosmogenic nuclides, {sup 36}Cl (half-life = 3.01 x 10{sup 5} yr), {sup 26}Al (7.05 x 10{sup 5} yr), and {sup 10}Be (1.5 x 10{sup 6} yr) in NWA 032 and Dhofar 081. The measurements of {sup 41}Ca (1.04 x 10{sup 5} yr) are in progress