  We investigate the consequences of flat, dark-matter dominated cosmogonies
with hybrid isocurvature and adiabatic initial perturbations and with
Harrison-Zel'dovich primordial spectrum normalised to the $COBE$-DMR two-year
measurements. We show that whilst the $COBE$-DMR data alone shows no preference
for a specific admixture of these modes, acceptable combinations are strongly
constrained by other observational data. Nevertheless, in some cases a suitable
mixture of these modes still may be used in an attempt to avoid some of the
observed problems of purely adiabatic models. Specifically, we consider
critical density, cold dark matter (CDM) and mixed dark matter (MDM) models.
