  We initiate a study of E-semigroups over convex cones. We prove a structure
theorem for E-semigroups which leave the algebra of compact operators
invariant. Then we study in detail the CCR flows, E$_0$semigroups constructed
from isometric representations, by describing their units and gauge groups. We
exhibit an uncountable family of $2-$parameter CCR flows, containing mutually
non-cocycle-conjugate E$_0$-$semigroups.
