[en] Fully periodic boundary conditions are incorporated into a gridless cosmological N-body code using the Ewald method. It is shown that the linear evolution of density fluctuations agrees well with analytic calculations, contrary to the case of quasi-periodic boundary conditions where the fundamental mode grows too rapidly. The implementation of fully periodic boundaries is of particular importance to relative comparisons of methods based on hierarchical tree algorithms and more traditional schemes using Fourier techniques such as PM and P³M codes. (author)