A high-resolution, ultrasonic (12–89 MHz) acoustic impedance technique has been used to investigate the order parameter collective modes in superfluid3He-B over a pressure range of 0–15 bar and in magnetic fields up to 180 mT. In agreement with earlier experiments, theJ=2 real squashing mode has been observed to split into five components in small magnetic fields. However, contrary to earlier theoretical estimates, the Zeeman shifts have been found to become extremely nonlinear as the magnetic field is increased. The extent of this nonlinearity is largest at low pressures and at temperatures close toTc. In comparison with recent theoretical work, the nonlinear Zeeman shifts may be explained as a result of two effects. First, there is a significant distortion of the B-phase energy gap in large magnetic fields. Second, there is an important coupling between the sameJzsubstates of the differentJ modes. In this sense the nonlinear evolution of the real squashing mode constitutes the observation of the Paschen-Back effect in3He-B. A comparison of the observed Zeeman shifts with theoretical expressions has yielded information about particle-particle and particle-hole interaction effects in the superfluid. In the limitT → 0 and above a threshold field, the real squashing mode has been found to possess additional structure. TheJz=0 substate has been observed to split into a doublet. The separation between the two components of the doublet is of the order of 100–200 kHz and remains independent of the magnetic field. The origin of the doublet may be understood in terms of a recent theory which postulates a texture-dependent collective mode frequency. Further, at extremely small fields the effects due to dispersion of the real squashing modes have been found to be important. The magnitude of the dispersion-induced mode splitting in zero field is found to be consistent with theoretical predictions. TheJ=2 squashing mode has also been studied in the presence of a magnetic field. TheJz=0 state of the squashing mode is observed to shift to lower temperatures in a magnetic field. An additional field dependence of the observed acoustic impedance is interpreted as the evolution of theJz=−1, −2 states, but appears to be inconsistent with theoretical predictions.