We consider the problem of L 2-hedging of contingent claims in diffusion type models for securities markets. In contrast to a recent paper of Schweizer (1994) we insist on a non-negative wealth process corresponding to the optimal hedge portfolio. For this reason the usual projection methods cannot be applied. We give some applications of L 2-hedging in this setting including hedging under constraints, a problem of approximating the wealth process of a richer investor and a mean-variance version of it.