The kinetics of the reactions of nickel clusters with a deuterium molecule are studied, Dissociative chemisorption probabilities of the D(2) molecule on the small Ni(n) (n=7-10) clusters are computed by a quasi-classical molecular dynamics computer simulation technique. Structures of the clusters are obtained by an embedded-atom potential, and the interaction between the D(2) and Ni(n) is modelled by an LEPS (London-Eyring-Polanyi-Sato) function (energy surface). This analysis includes the chemisorption probabilities as functions of the impact parameter and of the relative translational energy of the D(2). The corresponding reactive cross-sections for the ground state of the molecule are calculated as functions of the collision energy and the size of the cluster. The role of the size of the clusters is examined. An indirect mechanism to the reaction, which involves formation of molecular adsorption as precursors to dissociative adsorption in the low collision energy region (less than 0.1eV), is observed. Results are discussed by comparing with the other similar theoretical and experimental studies. (C) 2000 Elsevier Science B.V. All rights reserved.