A negative resistance connected to a ``suitable'' resonant circuit (a current‐controlled negative resistance connected to a series‐tuned circuit, or a voltage‐controlled negative conductance connected to a parallel‐tuned circuit) constitutes an almost‐harmonic oscillator. In this paper the ``unsuitable'' connections (a current‐controlled negative resistance connected to a parallel‐tuned circuit, or a voltage‐controlled negative conductance connected to a series‐tuned circuit) are analyzed qualitatively in terms of variables leading to a single‐valued phase plane. Physical considerations, expressed in a jump condition, serve to connect different regions of analyticity of the differential equations of the circuit in this plane. The ``unsuitable'' connections cannot sustain almost‐harmonic oscillations, and their theoretically possible relaxation oscillations are unstable; they yield bistable circuits.