Summary. In this paper we consider some different techniques allowing to construct asymptotically efficient estimators in point process models. In particular we establish L2-differentiability for point processes with multiplicative intensities and thus can apply Hadamard differentiability techniques for the i.i.d. case. In the second part of the paper we extend some properties of differentiable functionals known from the i.i.d. situation to general LAN models of point processes. We establish the LAN condition for point processes with differentiable intensities and as consequence obtain optimality of various estimators in general intensity models