In the doctoral thesis, a passive hybrid battery and supercapacitor system (HBSS) is elaborated on. The passive hybrid system of the battery and supercapacitor is represented by the Kirchhoff circuit model of the first order. The load is modelled as a current sink. The waveform of the load current is represented as a series of rectangular pulses with a superimposed constant current. Based on the presented model, analytical expressions that accurately describe the HBSS behaviour during the transient and steady state were derived. An auxiliary parameter of the passive hybrid system of the battery and supercapacitor is defined, which establishes a functional relationship between the internal resistances of the system and the current-voltage conditions and losses for the purpose of the simpler analysis during the dynamic loading of the system. Also, a novel set of analytical expressions is introduced for the analysis of energy efficiency of the passive HBSS in relation to the stand-alone battery systems (SABS). Using the proposed expressions, energy efficiency of the passive HBSS was analysed for different dynamic load parameters. The analysis showed that in cases where the dynamic component of the load current is a very small part of the total load current, or slowly varying load currents, the passive HBSS, in relation to the SABS, has no advantages in terms of energy efficiency. The analysis resulted in an interval of the battery and supercapacitor parameters which is optimal for the sizing of the passive HBSS from a techno-economic aspect. In the doctoral thesis, the voltage equalisation procedure based on supercapacitor switching was presented for the first time as a Markov chain. This was done in order to analyse the influence of Kirchhoff circuit model parameters and switching frequency on the degree of voltage uniformity along the series connection of the supercapacitor. The presented approach based on the application of Markov chains proved to be suitable for analysing the operation of the voltage equaliser based on supercapacitor switching and for determining its important parameters.