One of the long-term challenges of programming by demonstration is achieving generality, i.e. automatically adapting the reproduced behavior to novel situations. A common approach for achieving generality is to learn parameterizable skills from multiple demonstrations for different situations. In this paper, we generalize recent approaches on learning parameterizable skills based on dynamical movement primitives (DMPs), such that task parameters are also passed as inputs to the function approximator of the DMP. This leads to a more general, flexible, and compact representation of parameterizable skills, as demonstrated by our empirical evaluation on the iCub and Meka humanoid robots.