[en] We consider the superconformal extension of R2-actions in 6 and 10 dimensions. We show that the fields of the conformal multiplet alone admit a one parameter family of R2-actions of the form phi[Rsub(μνab)2 + α(Rsub(μνab)2- 4 Rsub(μa)2 + R2)]. In d=6 we give the supersymmetric action for α=0, while for α not=0 we give partial results. We show that for α=0 and in a conformal gauge the 3-form field Hsub(μνrho) has a natural torsion interpretation. In d=10 we find similar results (except the torsion interpretation) up to variations containing the 7-form field strength. (author)