  We present a study of open inflation cosmological scenarios in which cosmic
strings form betwen the two inflationary epochs. It is shown that in these
models strings are stretched outside the horizon due to the inflationary
expansion but must necessarily re-enter the horizon before the epoch of equal
matter and radiation densities. We determine the power spectrum of cold dark
matter perturbations in these hybrid models, finding good agreement with
observations for values of $\Gamma=\Omega_0h\sim0.3$ and comparable
contributions from the active and passive sources to the CMB. Finally, we
briefly discuss other cosmological consequences of these models.
