It is shown that any theory of gravitation with a nonlinear Lagrangian depending on the Ricci tensor is equivalent to the Einstein theory of gravitation interacting with additional matter fields.Consider a metric theory of gravitation (possibly interacting with a bosonic matter field 4 A ) based on a nonlinear Lagrangian:where L,,, is a matter Lagrangian, R,, =R,,(g) is the Ricci curvature of a metric tensor g, y 1s the Levi-Civita connection of g, and ~= 8 . n G is the gravitational constant. The choice of the linear function F(g,,,R,, ) = R =R,,g@"(2)leads to the standard Einstein theory. Recently, e.g., alot of interest has been devoted to quadratic Lagrangians,'which will be discussed in the sequel as a special case of our problem. Now we consider a general nonlinear case (1). The Euler-Lagrange equations,form a system of fourth-order differential equations for the metric g unless F is linear. Equation (4) can be rewritten as where by D we denote the covariant derivative with respect to y. We introduce the auxiliary quantity A,"=( -detg ) ' / 2 a~/ a~, vwhich is at the moment merely an abbreviation for a tensor density built up for gpv and R,,:The specific form of relation (8) depends on the choice of the function F, i.e., on the choice of our Lagrangian (1) [e.g., for a quadratic Lagrangian (3) Xpv depends linearly on R,,; this example will be discussed in detail]. Relation (8) is a second-order differential equation for g,,. This enables us to rewrite Eq. (6) asThe above fourth-order differential equation for g,, is equivalent to the system (8) and (9) of second-order differential equations for independent quantities g,, andXpv. It is interesting to notice that the second-order differential operator acting on A, " is universal and does not depend on a special choice of a Lagrangian function (1). This leads to the following result, which we prove in