  We write arbitrary separable nuclear C*-algebras as limits of inductive
systems of finite-dimensional C*-algebras with completely positive connecting
maps. The characteristic feature of such CPC*-systems is that the maps become
more and more orthogonality preserving. This condition makes it possible to
equip the limit, a priori only an operator space, with a multiplication turning
it into a C*-algebra. Our concept generalizes the NF systems of Blackadar and
Kirchberg beyond the quasidiagonal case.
