This paper discusses an efficient implementation of the generation of order conditions for the construction of exponential integrators like exponential splitting and Magnus-type methods in the computer algebra system Maple. At the core of this implementation is a new algorithm for the computation of coefficients of words in the formal expansion of the local error of the integrator. The underlying theoretical background including an analysis of the structure of the local error is briefly reviewed. As an application the coefficients of all 8th order self-adjoint commutator-free Magnus-type integrators involving the minimum number of 8 exponentials are computed.Keywords: Splitting methods • Magnus-type integrators • Local error • Order conditions • Computer algebra. 4 For our considerations, it is sufficient to discuss linear problems. The algebraic structure underlying method construction is the same for nonlinear problems due to the calculus of Lie derivatives [8, Section III.5.1]. 5 We have used Maple 18, Maple is a trademark of Waterloo Maple Inc.