A physically justifiable mathematical model is proposed for a class of current-controlled, negative resistance oscillators having terminal characteristics which are poorly represented by the van der Pol, Scott, and Ceschia-Zecchin equations. Such resonators are typified by the monolithic emitter-coupled astable multivibrator (ECAM). A unique, three-parameter equation, based on the inverse hyperbolic tangent, is matched to the ECAM voltage-current curve. Using the method of Kryloff and Bogoliuboff, the transient and steady-state behavior of the ECAM is derived for oscillation with single-mode and double-mode LCR networks under quasi-linear conditions. An expression for the time of amplitude build-up and decay is derived. A phase plane is constructed for the double-mode case, yielding a system apparently free of simultaneous modes. The validity of the model is experimentally verified for quartz-controlled ECAM devices. The analysis results are extendable ton resonant modes and may be generalized to voltage-controlled devices.