  We find the full symmetries of the Wheeler-DeWitt equation for the Hawking
and Page wormhole model and an axion-dilaton string cosmology. We show that the
Wheeler-DeWitt Hamiltonian admits an U(1,1) hidden symmetry for the Hawking and
Page model and U(2,1) for the axion-dilaton string cosmology. If we consider
the existence of matter-energy renormalization, for each of these models we
find that the Wheeler-DeWitt Hamiltonian accept an additional SL(2,R) dynamical
symmetry. In this case, we show that the SL(2,R) dynamical symmetry generators
transform the states from one energy Hilbert eigensubspace to another. Some new
wormhole type-solutions for both models are found.
