We present an approach to static and dynamical properties of holes and spins in weakly doped antiferromagnets in two dimensions. The calculations are based on a recently introduced cumulant approach to ground-state properties of correlated electronic systems. The present method allows us to evaluate hole and spin-wave dispersion relations by considering hole or spin excitations of the ground state. Usually, these dispersions are found from time-dependent correlation functions. To demonstrate the ability of the approach we first derive the dispersion relation for the lowest single hole excitation at half-filling. However, the main purpose of this paper is to focus on the mutual influence of mobile holes and spin waves in the weakly doped system. It is shown that low-energy spin excitations strongly admix to the ground state. The coupling of spin waves and holes leads to a strong suppression of the staggered magnetization which cannot be explained by a simple rigid-band picture for the hole quasiparticles. Also the experimentally observed doping dependence of the spin-wave excitation energies can be understood within our formalism.