  We define the secondary invariants L^2- eta and -rho forms for families of
generalized Dirac operators on normal coverings of fibre bundles. On the
covering family we assume transversally smooth spectral projections, and
Novikov--Shubin invariants bigger than 3(dim B+1) to treat the large time
asymptotic for general operators. In the particular case of a bundle of spin
manifolds, we study the L^2- rho class in relation to the space of positive
scalar curvature vertical metrics.
