This paper is concerned about power series expansions for hypergeometric functions in two variables. The usual power series representations for such functions have limited range of validity. Of particular interest is the case when the magnitude of one of the variables becomes large. Using a Barnes-type integral representation the region of convergence is transferred to the desired domain. The poles that occur in the Barnes-type integral are assumed to be simple. Thus explicit expansions are obtained for each of the fourteen hypergeometric functions that belong to this class.