  We consider two special types of double pendula, with the motion of masses
restricted to various surfaces. In order to get quick insight into the dynamics
of the considered systems the Poincar\'e cross sections as well as bifurcation
diagrams have been used. The numerical computations show that both models are
chaotic which suggest that they are not integrable. We give an analytic proof
of this fact checking the properties of the differential Galois group of the
system's variational equations along a particular non-equilibrium solution.
