We identify Melrose’s suspended algebra of pseudodifferential operators with a subalgebra of the algebra of parametric pseudodifferential operators with parameter space
; ;. For a general algebra of parametric pseudodifferential operators, where the parameter space may now be a cone ; ;, we construct a unique “symbol valued trace”, which extends the ; ;–trace on operators of small order. This construction is in the spirit of a trace due to Kontsevich and Vishik in the nonparametric case. Our trace allows us to construct various trace functionals in a systematic way. Furthermore, we study the higher–dimensional eta–invariants on algebras with parameter space ; ;. Using Clifford representations we construct for each first order elliptic differential operator a natural family of parametric pseudodifferential operators over ; ;. The eta–invariant of this family coincides with the spectral eta–invariant of the operator.