Abstract This paper gives a detailed account of both theoretical and numerical investigations which have been conducted in the application of A-stable algorithms to neutron kinetics problems. It is broadly divided into three sections. General considerations on desirable features of a reactor dynamics code are followed by the theoretical background. In order to be self-contained, the stability properties of one-step methods are recalled with emphasis on the A-stability concept introduced by Dahlquist. An algorithm is described, based on the interpolation of exp( z) in the unit disc of the complex plane, which generates A-stable schemes w nn ( z), ( n= 1,…) with so-called ‘spectral matching’ properties. Practical reasons limit to w 11 ( z) its use for the integration of the kinetics equations and the analytical properties of this first order rational approximation to the exponential function are studied. A second class of suitable integration schemes is made of the implicit Runge-Kutta (IRK) family, particularly the subclass of diagonally implicit Runge-Kutta (DIRK) methods which are factorizable. Finally, the numerical results obtained with these algorithms are discussed on a set of four point kinetics problems for both fast and thermal-type reactors.