Mg in two Allende Ca-Al rich inclusions shows large isotopic, mass-dependent fractionation which enriched the heavier isotopes. After normalization, Mg in these inclusions shows negative Δ26Mg which appears to require the presence of nuclear effects in Mg distinct from 26Al decay. The Mg mass fractionation is correlated with distinct but smaller fractionation effects for O reported by Clayton and Mayeda for the same inclusions (see companion paper). The observation of distinctive but uniform Mg isotopic composition in different phases within single Allende inclusions indicates that nuclear effects in O and Mg are not due to the entrapment of interstellar carrier grains as discrete entities, which are preserved as remnants, but are instead due to a homogenized mixture of components of extraordinary isotopic composition mixed with a component of ordinary solar system material and subjected to isotopic fractionation. The distinct O isotopic composition of different phases within a single inclusion is believed to be due to incomplete back-reaction of the higher temperature condensates with a cooler solar nebula of ''normal '' composition. The processes responsible for the O and Mg nuclear effects and the astrophysical site of their occurrence remain undefined.