The conventional squeezed states of quantum optics, which can be thought of as generalized coherent states for the algebra SU(1,1), are dynamically generated by single-mode hamiltonians characterized by two-photon process interactions. By the explicit construction of a (highly non-linear) faithful realization of the group [ ] of automorphisms of SU(1,1), such hamiltonians are shown to be equivalent — up just to elements of [ ] — to that describing quantum mechanically a damped oscillator.