1. The maltase and glucoamylase activities of acid α-glucosidase purified from rabbit muscle exhibited marked differences in certain physicochemical properties. These included pH stability, inactivation by thiol-group reagents, inhibition by αα-trehalose, methyl α-d-glucoside, sucrose, turanose, polyols, glucono-δ-lactone and monosaccharides, pH optimum and the kinetics and pH-dependence of cation activation. 2. The results are interpreted in terms of the existence of at least two specific substrate-binding sites or sub-sites. One site is specific for the binding of maltose and probably other oligosaccharides. The second site binds polysaccharides such as glycogen. 3. The sites appear to be in close proximity, since glycogen and maltose are mutually inhibitory substrates and interact directly in transglucosylation reactions. 4. Acid α-glucosidase exhibited intrinsic transglucosylase activity. The enzyme catalysed glucosyl-transfer reactions from [14C]maltose (donor substrate) to polysaccharides (glycogen and pullulan) and to maltose itself (disproportionation). The pH optimum was 5.1, with a shoulder or secondary activity peak at pH5.4. The glucose transferred to glycogen was attached by α-1,4- and α-1,6-linkages. Three major oligosaccharide products of enzyme action on maltose (disproportionation) were detected. 5. The kinetics of enzyme action on [14C]maltose showed that the rate of transglucosylation increased in a sigmoidal fashion as a function of substrate concentration, approximately in parallel with a decrease in the rate of glucose release. 6. The results are interpreted to imply competitive interaction at a specific binding site between maltose and water as glucosyl acceptors. 7. The results are discussed in terms of the possible existence of multiple subgroups of glycogen-storage disease type II.