  We analyse the prospects for constructing hybrid models of inflation that
provide a dynamical realisation of the apparent closeness between the
supersymmetric GUT scale and the possible scale of cosmological inflation. In
the first place, we consider models based on the flipped SU(5)$\times$U(1)
gauge group, which has no magnetic monopoles. In one model, the inflaton is
identified with a sneutrino field, and in the other model it is a gauge
singlet. In both cases we find regions of the model parameter spaces that are
compatible with the experimental magnitudes of the scalar perturbations, $A_s$,
and the tilt in the scalar perturbation spectrum, $n_s$, as well as with an
indicative upper limit on the tensor-to-scalar perturbation ratio, $r$. We also
discuss embeddings of these models into SO(10), which is broken at a higher
scale so that its monopoles are inflated away.
