Volterra series expansions represent an important model for the representation, analysis and synthesis of nonlinear dynamical systems. However, a significant problem with this approach to system identification is that the number of terms required to be estimated grows exponentially with the order of the expansion. In practice, therefore, the Volterra series is typically truncated to consist of, at most, second degree terms only. In this paper it is shown how the ideas of reproducing kernel Hilbert spaces (RKHS) can be applied to provide a practicable solution to the problem of estimating Volterra series. The approach is based on solving for the Volterra series in a linearised feature space (corresponding to the Volterra series) which leads to a more parsimonious estimation problem.