Electric currents are present in the coronae above solar active regions, producing nonpotential magnetic fields that can be approximated as nonlinear force-free fields (NLFFFs). In this paper NLFFF models for two active regions observed in 2002 June are presented. The models are based on magnetograms from SOHO MDI and are constrained by nonpotential structures seen in BBSO Hα images and TRACE EUV images. The models are constructed using the flux rope insertion method. We find that the axial fluxes of the flux ropes are well constrained by the observations. The flux ropes are only weakly twisted, and electric currents flow mainly at the interface between the flux rope and its surroundings. In one case, the flux rope is anchored with both ends in the active region; in the other case, the flux rope extends to the neighboring quiet Sun. We find that the magnetic fields in these active regions are close to an eruptive state: the axial flux in the flux ropes is close to the upper limit for eruption. We also derive estimates for magnetic free energy and helicity in these regions.