A multifrequency power circuit of an NMR coil, includes two power or transmission line segments called principal line segments, each including a segment of a conductor that is attached to the coil, which attached segments together with the coil constitute a first oscillating circuit that exhibits a determined resonance frequency. The principal line segments consist of controlled-impedance multiconductor line segments, each including at least one other conductor segment that is not attached to coil and that extends into the principal line segment beside corresponding respectively attached conductor segment and that exhibits with the latter a capacitive coupling that is distributed along segments located beside or opposite the conductors. These non-attached conductor segments, together with the coil, attached conductor segments and non-attached conductor segments, and optionally with additional power line segments connected to the non-attached conductor segments, form at least one additional oscillating circuit that has a different resonance frequency.