Abstract. The topological string captures certain superstring amplitudes which are also encoded in the underlying string effective action. However, unlike the topological string free energy, the N=2 string effective action including higher derivative couplings, is not defined in terms of duality covariant variables. We shall discuss this in the context of N=2 supergravity by introducing the Hesse potential defined in terms of duality covariant variables and is related by a Legendre transformation to the function that encodes the effective action. The non-holomorphic deformations of this function have been included for obtain results for the more general case. It is then demonstrated that the Hesse potential contains a unique subsector which can be identified with topological string free energy and it satisfies the holomorphic anomaly equation of topological string theory.