To study the nonlinear regime of cosmic structure formation, Newtonian N-body simulations are an established standard tool. Our aim is to take a first step beyond the Newtonian limit towards a dynamical description of space-time. This will allow one to include intrinsically relativistic sources into the game (e.g. "clustering" dark energy, cosmic strings...) and also to address the issue of backreaction. I will present a perturbative approach which is designed to take into account the most important relativistic effects while maintaining a moderate level of complexity and conceptual challenge. Once the problem is specified, I will discuss strategies for the algorithmic solution and present some preliminary numerical results.