A real linear space L of dimension is called an n-inner product space if it is equipped with an n-inner product , . Every such space has a natural topology defined by the n-norm . This paper is a continuation of previous investigations of n-inner product spaces by the same author [Math. Nachr. 140, 299-319 (1989; Zbl 0673.46012)]. Here orthogonal and orthonormal sets, generalized Fourier series expansions and representations of n- inner products are studied. Suppose the natural topology of L agrees with the topology given by the norm
where are arbitrary elements of L satisfying . Then theorems on convergence of generalized Fourier series and generalized Parseval equality analogous to those in ordinary inner product spaces can be proved.