Weight-average elution volumes of sulphatase A (an arylsulphate sulphohydrolase, EC 3.1.6.1) from Sephadex G-200 have been determined as functions of protein concentration, pH, ionic strength and temperature. The results are used to calculate the apparent association equilibrium constants for tetramer formation and the associated standard-state thermodynamic parameters. While the apparent association constant decreased from 10(28) to 10(21) M-3 on increasing the pH from 4.5 to 5.6 at ionic strength 0.1, at any particular pH value studied it was relatively insensitive to temperature variation so that deltaH is close to zero and tetramer formation in solution is associated with a positive entropy change. At pH 5.0, increasing the ionic strength from 0.1 to 2 decreased the association constant by a factor of 100. Methylumbelliferone sulphate has no effect on the association of sulphatase A. The equilibrium results are used to define the degree of association of sulphatase A likely to encountered in experiments designed to elucidate its kinetic properties. In the liver lysosome, the tetramer is probably the dominant species. The monomer and tetramer of sulphatase A have similar, or identical, specific activities with nitrocatechol sulphate and 4-methylumbelliferone sulphate as substrates. With nitrocatechol sulphate, sulphatase A shows Michaelis kinetics under conditions where the monomer is the dominant species and non-Michaelis kinetics where the tetramer is dominant. There is apparently a negative cooperativity between the monomer units in the tetramer. In 2 mM sodium taurodeoxycholate and 0.035 M MnCl2, but not in 0.1 M NaCl, the tetramer shows Michaelis kinetics. This is not due to dissociation of the tetramer. The critical micellar concentration of sodium taurodeoxycholate is about 0.8 mM in both 0.1 M NaCl and 0.035 M McCl2 but the aggregation number is greater in the latter.