Let X be a space with free loop space LX. The string cohomology of X is by definition the equivariant cohomology of LX with respect to the action of the circle group. For Z/2 coefficients M. Bokstedt and I defined a functor l which approximates the string cohomology of X when applied to the ordinary cohomology of X. In my talk I will introduce a spectral sequence which converges towards string cohomology of simply connected spaces. The E_2-term is given by the non Abelian derived functors of l. I will explain why it is likely that this spectral sequence collapses for a large class of spaces.