We present f(R) theories of ten-dimensional supergravities, including the fermionic sector up to the quadratic order in fermion fields. They are obtained by performing the conformal scaling on the usual supergravities to the f(R) frame in which the dilaton becomes an auxiliary field and can be integrated out. The f(R) frame coincides with that of M-theory, D2-branes or NS-NS 5-branes. We study various BPS p-brane solutions and their near-horizon AdS \times sphere geometries in the context of the f(R) theories. We find that new solutions emerge with global structures that do not exist in the corresponding solutions of the original supergravity description. In lower dimensions, We construct the f(R) theory of N=2, D=5 gauged supergravity with a vector multiplet, and that for the four-dimensional U(1)^4 gauged theory with three vector fields set equal. We find that some previously-known BPS singular "superstars" become wormholes in the f(R) theories. We also construct a large class of f(R) (gauged) pseudo-supergravities. In addition we show that the breathing mode in the Kaluza-Klein reduction of Gauss-Bonnet gravity on S^1 is an auxiliary field and can be integrated out.

Latex, 46 pages