Abstract. Hybrid inflation is a natural scenario in the absence of supersymmetry. In the context of supergravity, however, it has to face the naturalness problems of the initial conditions and of the adequate suppression of the inflaton mass. Both can be successfully addressed in a class of models involving Kähler potentials associated with products of SU (1, 1)/U (1) Kähler manifolds and "decoupled" fields acquiring large vacuum expectation values through D-terms.Inflation offers an elegant solution to many cosmological problems [1]. However, "natural" realizations of the inflationary scenario are hard to find. "New" and "chaotic" inflation [1] invoke a very weakly coupled scalar field, the inflaton, in order to reproduce the observed temperature fluctuations ∆T T [2] in the cosmic background radiation (CBR). To overcome this naturalness problem Linde proposed the "hybrid" inflationary scenario [3,4] involving a coupled system of (two) scalar fields which manages to produce the temperature fluctuations in the CBR with natural values of the coupling constants. This is achieved by exploiting the smallness in Planck scale units (M P / √ 8π ≃ 2.435515 × 10 18 GeV = 1 which are adopted throughout our disscusion) of the false vacuum energy density associated with the phase transition leading to the spontaneous breaking of a symmetry in the post-Planck era. In the case that the broken symmetry is a gauge symmetry one of the (two) scalar fields involved is not a gauge singlet.Linde's potential is given by