  We investigate $E_0-$semigroups on general factors, which are not necessarily
of type I, and analyse associated invariants like product systems, super
product systems etc. By tensoring $E_0-$semigroups on type I factors with
$E_0-$semigroups on type II$_1$ factor, we produce several families (both
countable and uncountable), consisting of mutually non-cocycle-conjugate of
$E_0-$semigroups on the hyperfinite II$_\infty$ factor. Using CCR
representations associated with quasi-free states, we construct for the first
time, uncountable families consisting of mutually non-cocycle-conjugate
$E_0-$semigroups on all type III$_\lambda$ factors, for $\lambda \in (0,1]$.
