Physical states for non-linear SO(N) strings

We study some low-lying physical states in a superstring theory based on the quadratically non-linear $SO(N)$--extended superconformal algebra. In the realisation of the algebra that we use, all the physical states are discrete, analogous to the situation in a one-scalar bosonic string. The BRST operator for the $N=3$ case needs to be treated separately, and its construction is given here.