Various causes for negative differential conductance in transport through an interacting double quantum dot are investigated. Particular focus is given to the interplay between the renormalization of the energy levels due to the coupling to the leads and the decoherence of the states. The calculations are performed within a basis of many-particle eigenstates and we consider the dynamics given by the von Neumann equation taking into account also processes beyond sequential tunneling. A systematic comparison between the levels of approximation and also with different formalisms is performed. It is found that the current is qualitatively well described by sequential processes as long as the temperature is larger than the level broadening induced by the contacts.