  We perform a general algebraic analysis on the possibility of realising
slow-roll inflation in the moduli sector of string models. This problem turns
out to be very closely related to the characterisation of models admitting
metastable vacua with non-negative cosmological constant. In fact, we show that
the condition for the existence of viable inflationary trajectories is a
deformation of the condition for the existence of metastable de Sitter vacua.
This condition depends on the ratio between the scale of inflation and the
gravitino mass and becomes stronger as this parameter grows. After performing a
general study within arbitrary supergravity models, we analyse the implications
of our results in several examples. More concretely, in the case of heterotic
and orientifold string compactifications on a Calabi-Yau in the large volume
limit we show that there may exist fully viable models, allowing both for
inflation and stabilisation. Additionally, we show that subleading corrections
breaking the no-scale property shared by these models always allow for
slow-roll inflation but with an inflationary scale suppressed with respect to
the gravitino scale. A scale of inflation larger than the gravitino scale can
also be achieved under more restrictive circumstances and only for certain
types of compactifications.
