  We propose a twistor--like formulation of N=1, D=3,4,6 and 10 null
superstrings. The model possesses N=1 target space supersymmetry and n=D-2
local worldsheet supersymmetry, the latter replaces the kappa-symmetry of the
conventional approach to the strings. Adding a Wess--Zumino term to a null
superstring action we observe a string tension generation mechanism: the
induced worldsheet metric becomes non-degenerate and the resulting model turns
out to be classically equivalent to the heterotic string.
