The theory for all fundamental particles proposed earlier is further discussed and the higher hadron supermultiplets and the corresponding mass levels of the various spins and parities have been calculated. Each supermultiplet is designated by the principal quantum numbers N0 and N in the form [N0, N], where N0 and N refer to the dimension numbers of the groups SO(3,2) and U(3,1), respectively. The generators of the groups SO(3,2) and U(3.1) constitute the algebraic basis of the fundamental wave equation. The results of the theory and the experimental data on hadron masses are found to be in excellent accord. The parities of the particles are obtained unambiguously, and the theory predicts 2- and higher-spin mesons in addition to known ones. In the extreme limit of the parameters ρ and λ where ρ=0, λ=0, the [5,4], [5,6], [5,10], [5,15] levels each describe the photon, while the level [5,20] yields the graviton as a massless 2+ particle. The limit ρ=0, λ=0 for the baryon and the lepton supermultiplets [4b,N], [4l,N], respectively, when coupled together implies the existence, at the lowest levels [4b,4] and [4l,4], of two s=12 two-component neutrinos. Higher-spin massive and massless leptons are also predicted.