  We consider a double-inflationary model with two massive scalar fields
interacting only gravitationally in the context of a flat cold dark matter
(CDM) Universe. The cosmic microwave background (CMB) temperature anisotropies
produced in this theory are investigated in great details for a window of
parameters where the density fluctuation power spectrum P(k) is in good
agreement with observations. The first Doppler (``acoustic'') peak is a crucial
test for this model as well as for other models. For the ``standard'' values of
the cosmological parameters of CDM, our model is excluded if the height of the
Doppler peak is sensibly higher than about three times the Sachs-Wolfe plateau.
