Equations for calculating the initial rates of enzyme activation (v(a)) and also of the nontrivial types of enzyme inhibition (v(i)) unavailable in enzyme kinetics were derived. Analysis of the equations showed that it is incorrect to apply the (1/v(i); i) coordinates to data processing of types: I-i and IIi' of biparametrically coordinated and biparametrically discoordinated enzyme inhibition, respectively. New possibilities of data analysis of enzyme activation are considered. Examples illustrating the calculation of the K-IIIa and K-IVa constants of the catalytic (IIIa) and associative (IVa) types of enzyme activation are presented. (C) 2002 Published by Elsevier Ltd.