Some transients in linear a.c. circuits can be advantageously described by a slowly varying phasor. This is true also for a quasilinearRLCnetwork, linearised at the point of near-resonance operation, for a small-perturbation stability analysis. The linearisation of a nonanalytical complex function indicates a tensorial relationship between the variables, but this is not uncommon in other well known electric-circuit applications such as synchronous machines and current transformers. The stability analysis is performed by calculating, step by step, the trajectory of a small initial perturbance phasor. It is illustrated by the example of a seriesRLCcircuit and a capacitive voltage divider with a quasilinear inductive load.