This paper presents a Hilbert-transform (HT) based approach to determine apparent power components in non-sinusoidal circuits with zero instantaneous power. Instantaneous current and voltage phasors, instantaneous active power, instantaneous reactive power, and instantaneous apparent power are also, defined. The properties of the determined power related quantities are discussed. The proposed approach is applicable to sinusoidal and non-sinusoidal systems. A study case of a circuit with square wave voltage and current and zero instantaneous power is examined