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We study some low-lying physical states in a superstring theory based on thequadratically non-linear $SO(N)$--extended superconformal algebra. In therealisation of the algebra that we use, all the physical states are discrete,analogous to the situation in a one-scalar bosonic string. The BRST operatorfor the $N=3$ case needs to be treated separately, and its construction isgiven here.Comment: 9 pages, Latex, no figure

Physical states for nonlinear SO(N) superstrings