We consider the issue of classification of functional data and, in particular, we deal with the problem of curve clustering when curves are misaligned. In the proposed setting, we aim at jointly aligning and clustering the curves, via the solution of an optimization problem. We describe an iterative procedure for the solution of the optimization problem, and we detail two alternative specifications of the procedure, a k-mean version and a k-medoid version. We illustrate via applications to real data the robustness of the alignment and clustering procedure under the different specifications.