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We write in superspace the lagrangian containing the fourth power of the Weyltensor in the "old minimal" d=4, N=2 supergravity, without local SO(2)symmetry. Using gauge completion, we analyze the lagrangian in components. Wefind out that the auxiliary fields which belong to the Weyl and compensatingvector multiplets have derivative terms and therefore cannot be eliminatedon-shell. Only the auxiliary fields which belong to the compensating nonlinearmultiplet do not get derivatives and could still be eliminated; we check thatthis is possible in the leading terms of the lagrangian. We compare this resultto the similar one of "old minimal" N=1 supergravity and we comment on possiblegeneralizations to other versions of N=1,2 supergravity.Comment: 31 pages, no figures. Minor corrections. Details of the full  calculation included as an appendix. Reference adde

Four dimensional ``old minimal'' Script N = 2 supersymmetrization of Script R4

Four dimensional ``old minimal'' Script N = 2 supersymmetrization of Script R⁴