Electricity is central to socioeconomic growth and development of any economy. And, the electrical power sector of many economies has witnessed reforms in recent time, transforming into competitive and or oligopolistic market structure. In any case, energy pricing subsist as a challenge across the power value chain. This study focused identifying the determinants of market power of energy distributing operation and rural area consumers in the power retail market in Nigeria's present oligopolistic power market structure. Adopting a production function model and econometric analysis of selected power sector time series variables between 2000-2017, the study discovered that electrical power generation, rural electricity access and energy consumption in Nigeria are essential determinants but do not ultimately and significantly determine market power of competing firms in the electric power market in Nigeria. It concluded that evidence of the importance of market power for competing firms in the electric power conduct in terms of energy pricing and cost decisions is auspicious considering their prevailing market challenges. The study therefore recommend amongst others recapitalization by energy distribution firms, exclusive regional or sub regional power chain structural transformation, efficient and effective energy supply, elicitation of market information/data for control, improvement, competition and researches in the sector while future research on market power in electrical power market is encourage on assumptions. Contribution/ Originality: This study adds to existing literature on energy market pricing and structure by using econometric estimation technique and originates a model. It is also adds to few investigations on the subject matter in Nigeria by logical analysis, finding and documentation of determinants of market power of electrical power market.