We present a new treatment of 2-spinors and twistors, using the spacetime algebra. The key rôle of bilinear covariants is emphasized. As a by-product, an explicit representation is found, composed entirely of real spacetime vectors, for the Grassmann entities of supersymmetric field theory.

A. N. Lasenby, C. J. L. Doran and S. F. Gull, **2-spinors, Twistors and Supersymmetry in the Spacetime Algebra, **In Z. Oziewicz, A. Borowiec and B. Jancewicz, editors, *Spinors, Twistors, Clifford Algebras and Quantum Deformations* (Kluwer Academic, Dordrecht, 1993), p.233-245.