A novel model order reduction method for efficient analysis of linear eddy-current problems is proposed in which the quasi-static electromagnetic fields are expressed by a weighted sum of a sequence of static electric- A nd magnetic-field modes. The modes are calculated sequentially by static electric and static magnetic computations using the conventional finite-element method, and the time-dependent weights are the voltages and currents of an equivalent Cauer ladder network of the problem. In this paper, the formulation of the method and a numerical test problem are presented, and the accuracy and enormous efficiency of the method are demonstrated by solving a 3-D nonlinear inductor model with a voltage excitation by a dc-dc converter, linearized around the dc current using frozen differential permeability.