1. The ratio of ebgA-gene product of ebgC-gene product in the functional aggregate of ebg beta-galactosidases was determined to be 1:1 by isolation of the enzyme from bacteria grown on uniformly radiolabelled amino acids and separation of the subunits by gel-permeation chromatography under denaturing conditions. 2. This datum, taken together with a recalculation of the previous ultracentrifuge data [Hall (1976) J. Mol. Biol. 107, 71-84], analytical gel-permeation chromatography and electron microscopy, strongly suggests an alpha 4 beta 4 quaternary structure for the enzyme. 3. The second chemical step in the enzyme turnover sequence, hydrolysis of the galactosyl-enzyme intermediate, is markedly slower for ebgab, having both Asp-97----Asn and Trp-977----Cys changes in the large subunit, than for ebga (having only the first change) and ebgb (having only the second), and is so slow as to be rate-determining even for an S-glycoside, beta-D-galactopyranosyl thiopicrate, as is shown by nucleophilic competition with methanol. 4. The selectivity of galactosyl-ebgab between water and methanol on a molar basis is 57, similar to the value for galactosyl-ebgb. 5. The equilibrium constant for the hydrolysis of lactose at 37 degrees C is 152 +/- 19 M, that for hydrolysis of allolactose is approx. 44 M and that for hydrolysis of lactulose is approx. 40 M. 6. A comparison of the free-energy profiles for the hydrolyses of lactose catalysed by the double mutant with those for the wild-type and the single mutants reveals that free-energy changes from the two mutations are not in general independently additive, but that the changes generally are in the direction predicted by the theory of Burbaum, Raines, Albery & Knowles [(1989) Biochemistry 28, 9283-9305] for an enzyme catalysing a thermodynamically irreversible reaction. 7. Michaelis-Menten parameters for the hydrolysis of six beta-D-galactopyranosylpyridinium ions and ten aryl beta-galactosides by ebgab were measured. 8. The derived beta 1g values are the same as those for ebgb (which has only the Trp-977----Cys change) and significantly different from those for ebgo (the wild-type enzyme) and ebga. 9. The alpha- and beta-deuterium secondary isotope effects on the hydrolysis of the galactosyl-enzyme of 1.08 and 1.00 are difficult to reconcile with the pyranose ring in this intermediate being in the 4C1 conformation.