  We construct the q-deformed version of two four-dimensional spin foam models,
the Euclidean and Lorentzian versions of the EPRL model. The q-deformed models
are based on the representation theory of two copies of U_q(su(2)) at a root of
unity and on the quantum Lorentz group with a real deformation parameter. For
both models we give a definition of the quantum EPRL intertwiners, study their
convergence and braiding properties and construct an amplitude for the
four-simplexes. We find that both of the resulting models are convergent.
