In this paper the problem of developing bidding strategies for the participants of dynamic oligopolistic electricity markets is studied. Attention is given to strategic bidding of load serving entities (LSE) in these markets. We model oligopolistic electricity markets as non-linear dynamical systems and use discrete-time Nash bidding strategies. We assume a Cournot model for our game, where the LSEs decide on demand quantities and the market price is the marginal cost of producing electricity. Attention is given to a problem, where the objective functions are quadratic in the deviations of trajectories from desired trajectories and quadratic in the control deviations from the nominal controls. It is assumed that each power marketer can estimate his/her competitors' benefit function coefficients. The optimal bidding strategies are developed mathematically using dynamic game theory. We deal with games that are non-linear in the state equations. We linearize these equations for complex non-linear oligopolistic electricity multi-markets and use discrete-time Nash strategies. We show that the actual dynamic excursions from the operating point where we linearize are small so that the linearization is valid. The developed algorithm is applied to an IEEE 14-bus power system. We show that the LSEs' expected profits are higher for our method than those for other methods in the literature (F. Wen, A.K. David, Optimal bidding strategies and modeling of imperfect information among competitive generators. IEEE Transactions on Power Systems, Vol. 16, No. 1, pp.15-21, Feb. 2001.