Magnetodielectric properties of magnetoactive elastomers comprising micrometer-sized iron particles dispersed in compliant elastomer matrices are experimentally studied in stepwise time-varying dc magnetic fields. It is found that imposition of magnetic field significantly increases both the effective lossless permittivity of these composite materials as well as their effective conductivity. These magnetodielectric effects are more pronounced for larger concentrations of soft-magnetic filler particles and softer elastomer matrices. The largest observed relative change of the effective dielectric constant in the maximum magnetic field of 0.57 T is of the order of 1000%. The largest observed absolute change of the loss tangent is approximately 0.8. The transient response of the magnetodielectric effect to a step magnetic-field excitation can be rather complex. It changes from a simple monotonic growth with time for small magnetic-field steps (<0.1 T) to a non-monotonic behavior with a significant rapidly appearing overshoot for large magnetic-field steps (>0.3 T). The settling time to the magnetic-field step excitation can reach roughly 1000 s and it depends on the applied magnetic field and sample composition. There is also significant hysteresis of the magnetodielectric effect on the externally applied magnetic field. These findings are attributed to the rearrangement of ferromagnetic filler particles in external magnetic fields. The results will be useful for understanding and predicting the transient behavior of magnetoactive elastomers in applications where the control magnetic field is time dependent. (C) 2017 Elsevier Ltd. All rights reserved.