The requirement of muscle phosphorylase for branched polysaccharide substrates was investigated by kinetic studies on semisynthetic branched saccharides. One series of saccharides was prepared from maltoheptose by oxidizing the reducing group to a carboxyl group and coupling this with an amino group of ethylenediamine. The resulting aminooligosaccharide was coupled with p-nitrophenyl esters of mono-, di-, tetra-, and polycarboxylic aicds to produce saccharides containing one, two, four, and approximately 52 maltodextrin chains per molecule. A similar series of saccharides was prepared from a heterogeneous maltodextrin of average chain length 11.7. Kinetic constants were determined for the reaction with phoshorylase a in the direction of chain elongation. Michaelis constants are equilibrium constants for dissociation of saccharide from the enzyme-AMP-glucose-1P-saccharide complex. The Michaelis constants, expressed in terms of the concentration of nonreducing end groups, are independent of maltodextrin chain length but decrease considerably as the number of chains per molecule increases. Maximum velocities do not differ greatly from that for glycogen. Among the synthetic saccharides, only the polymer behaves similarly to glycogen in exhiiting a decreasing reaction rate as the chains are elongated. The kinetic constants are quantitatively consistent with a model in which two chain termini from the same saccharide molecule bind to the phosphorylase molecule simultaniously, Differences in binding between saccharides having different numbers of equally accessible chains are caused solely by statistical factors in the equilibrium. Highly branched substrates bind better because of their greater multiplicity of two end-group pairs.