  The effects of the presence of $\Delta$-isobars in nuclear matter are studied
in the framework of relativistic mean-field theory. The existence of stable
nuclei at saturation density imposes constraints on the $\Delta$-isobar
self-energy and thereby on the mean-field coupling constants of the scalar and
vector mesons with $\Delta$-isobars. The range of possible values for the
scalar and vector coupling constants of $\Delta$-isobars with respect to the
nucleon coupling is investigated and compared to recent predictions of QCD
sum-rule calculations.
