We use the recent approach of N. Makarov and A. Poltoratski to give a criterion for completeness of systems of reproducing kernels in the model subspaces KΘ =H2 ⊖ΘH2 of the Hardy class H2 . As an application, we prove new results on stability of completeness with respect to small perturbations and obtain criteria for completeness in terms of certain densities. We also obtain a description of systems of reproducing kernels corresponding to real points which form a Riesz basis in a given model subspace generated by a meromorphic inner function Θ.