The study is intended to introduce an analytical approach to the transient problem of the nonlinear thermoelectric systems. The problem of predicting the output current as a function of time and that of predicting the temperature distributions in the thermoelectric elements as a function of both time and distance are determined with a given heat-input function. The analysis of the system is complicated by the following facts: 1) There exist several singularities in the system, and these singularities make the ordinary power expansions converge very slowly. 2) The boundary conditions of the initial transient and of the transient as the system approaches steady state yield two highly nonlinear differential equations of which the approximate solutions are very hard to obtain. The first problem is solved by using logarithmic and other transformations to remove the singularities. The second problem is overcome by applying the technique of the special expansion of Jacobi.