  A discussion of the number of degrees of freedom, and their dynamical
properties, in higher-derivative gravitational theories is presented. The
complete non-linear sigma model for these degrees of freedom is exhibited using
the method of auxiliary fields. As a by-product we present a consistent
non-linear coupling of a spin-2 tensor to gravitation. It is shown that
non-vanishing $(C_{\mu\nu\alpha\beta})^{2}$ terms arise in $N=1$, $D=4$
superstring Lagrangians due to one-loop radiative corrections with light field
internal lines.
