  We construct exact solutions representing a
Friedmann-Lema\^itre-Robsertson-Walker (FLRW) universe in a generalized hybrid
metric-Palatini theory. By writing the gravitational action in a scalar-tensor
representation, the new solutions are obtained by either making an ansatz on
the scale factor or on the effective potential. Among other relevant results,
we show that it is possible to obtain exponentially expanding solutions for
flat universes even when the cosmology is not purely vacuum. We then derive the
classes of actions for the original theory which generate these solutions.
