We consider joint Tikhonov- and Lavrentiev-regularization of control problems
with pointwise control- and state-constraints. We derive error estimates for
the error which is introduced by the Tikhonov regularization. With the help of
this results we show, that if the solution of the unconstrained problem has no
active constraints, the same holds for the Tikhonov-regularized solution if the
regularization parameter is small enough and a certain source condition is
fulfilled.