  Constrained Hamiltonian systems are investigated by using the Hamilton-Jacobi
method. Integration of a set of equations of motion and the action function is
discussed. It is shown that we have two types of integrable systems: a) ${\it
Partially integrable systems}$, where the set of equations of motion is only
integrable. b) {\it Completely integrable systems}, where the set of equations
of motion and the action function is integrable. Two examples are studied.
