Water-in-oil microemulsions are thermodynamically stable single-phase dispersions of water and surfactant within a continuous oil phase. The classical ternary system, based on the surfactant sodium bis(2-ethylhexyl)sulfosuccinate ('AOT'), water and an alkane such as n-heptane, is an optically transparent monodispersion of spherical water-droplets coated with a close-packed surfactant monolayer and the droplet radius is, to a good first approximation, directly proportional to the molar water: surfactant ratio, R. Enzymes dissolved in the water droplets retain activity and stability. These systems have attracted interest as media for biotransformations. Principally based upon studies in AOT-stabilized w/o microemulsions, a peculiar feature of the kinetics of enzyme-catalyzed reactions has long been apparent: the reaction rate characteristically increases from around zero at R=3, through a maximum, in the range R= 10-20, and thereafter decreases again, so that plots of rate vs. R are characteristically 'bell-shaped'. Furthermore, at optimal R, enzymes seem to be 'hyperactive', i.e., they are more active, by a modest but significant factor of 2-3-fold, than in aqueous solution. In this paper we propose the hypothesis that this kind of R-dependence arises because of the presence of freely mobile lone surfactant counterions (Na+) within the water-pool. These ions have no charge partners within the water pool and consequently have a high electrochemical potential. According to our model, lone counterions facilitate the hydrolysis of ester or amide substrates, for example, by stabilizing the tetrahedral intermediate formed during the reaction through ion-pairing with the carbonyl oxygen of the substrate, thus facilitating transfer of negative charge from the carbonyl carbon as it is attacked by the incoming nucleophile. An expression for the relationship between the concentration of free counterions in the water-pool and the compositional parameter R leads directly, through Debye-Hückel theory, to an expression for the relationship between the reaction rate and R, log k(R)= log k(o) + C(1/R)1/2 where k(R) is the rate constant at some finite R, k(o) is the rate constant extrapolated to R = infinity and C is an R-independent coefficient. For enzymes that display bell-shaped kinetics, such as bovine alpha-chymotrypsin and Chromobacterium viscosum lipase, the descending part of the plot (i.e. from optimal R to high R) obeys this equation very well. Inspection of the above equation shows that the rate constant, k(R) is greater than k(o). Furthermore it is reasonable to equate k(o) with k(aq), the aqueous solution value of k since the condition R = infinity may be equated with the condition of infinite dilution with respect to counterions, so eliminating their specific effect on the kinetics. It follows from the inequality, k(R) > k(o) approximately equal to k(aq), that the enzyme is 'hyperactive' in the microemulsion compared with aqueous solution. We show that this is indeed the case for the chymotrypsin-catalyzed hydrolysis of N-trans-cinnamoylimidazole and the lipase catalyzed hydrolysis of 4-nitrophenyl acetate. The tailing off of enzyme activity at low R (< 10) is most likely due to conformational immobilization, probably due to partial dehydration in these low-water preparations (water activity, a(w), drops off rapidly below R = 15). We show that the reaction of glycylglycine with 4-nitrophenyl acetate, a 'hyperactive' non-enzymic reaction, does not suffer from this effect and obeys the above equation across the whole range of R.