Surge arresters (SAs) are equipment applied to power systems in order to absorb the energy associated with overvoltages. Various diagnostic online monitoring methods of surge arrester are based on the decomposition of the measured leakage current into their capacitive and resistive components. The arrester’s resistive component of the leakage current, in particular, the third harmonic component, is known as to be directly related to the degree of degradation of the ZnO blocks. This paper proposes an online monitoring technique for the surge arrester under dry and pollution conditions when measuring either the total leakage current or both the internal and external leakage currents of three different types of surge arresters. The proposed technique of extracting the magnitudes and harmonic content of the measured voltage and current signals based on Prony analysis-Hilbert transform approach has proved its viability in handling both stationary and nonstationary signals with small number of samples. This technique can be easily adopted for new and strongly deteriorated SAs.