For 0 < p < 1, the notions of symmetric and asymmetric L p-intersection bodies were introduced by Haberl and Ludwig. Recently, Wang and Li defined the general L p-intersection bodies. In this paper, associated with the L p-dual affine surface areas, we give the extremum values of the general L p-intersection bodies. Moreover, a Brunn-Minkowski type inequality and a monotone inequality for the L p-dual affine surface area version of general L p-intersection bodies are established, respectively,