A non-perturbative theory of spectroscopy with pulsed laser excitation is presented with approximations that make calculation with long pulses as accessible as for short pulses. We apply it to continuum Raman scattering with a strong field and show that: (a) for a pulse shorter than the molecular dissociation time the range of excitation frequencies giving fluorescence-like emissions is greater than in a weak field, and (b) for a pulse that is longer than the molecular dissociation time, Raman-like emissions are dominant, with vibrational progressions over a wider range of excitation frequencies than in a weak field.