This paper discusses classical gravity theories with higher-order derivatives. Including terms like $ f_{\mu\nu}R^{\mu\nu}(-g)^{1/2} $ and $ \int R^{2}(-g)^{1/2} $ in the gravitational action leads to a class of effectively multimass gravity models. These models include, in addition to massless spin-two excitations, massive spin-two and massive scalar excitations, resulting in a total of eight degrees of freedom. The massive spin-two part of the field has negative energy. Specific ratios of the two new terms can eliminate either the massive tensor or the massive scalar, reducing the number of degrees of freedom. The static, linearized solutions of the field equations are combinations of Newtonian and Yukawa potentials. Observational evidence only weakly restricts the new masses. The acceptable static metric solutions in the full nonlinear theory are regular at the origin. The dynamical content of the linearized field is analyzed by reducing the fourth-order field equations to separated second-order equations, related by coupling to external sources in a fixed ratio. This analysis is carried out into the various helicity components using the transverse-traceless decomposition of the metric. The paper discusses the inclusion of higher-derivative terms in the gravitational Lagrangian, which stabilizes the divergence structure of gravity, allowing it to be renormalized. The early investigators thought that all classical tests of general relativity were automatically satisfied by these models. However, it was later pointed out that solutions of purely four-derivative models which do couple to a positive matter source are not asymptotically flat at infinity. The paper restricts itself to models derived from actions that include both the Hilbert action $ f(-g)^{1/2}R $ and the four-derivative terms. The action is written in the form $ I=-\int(-g)^{1/2}(\alpha R_{\mu\nu}R^{\mu\nu}-\beta R^{2}+\gamma\kappa^{-2}R) $, where $ \kappa^{2}=32\pi G $, and $ \alpha $, $ \beta $, and $ \gamma $ are dimensionless numbers. It is found that the correct physical value for $ \gamma $ is 2, as in Einstein's theory. The static spherically symmetric solutions to the field equations derived from (1.1) either reduce asymptotically to the sum of a Newtonian and two Yukawa potentials, or they are unbounded at infinity and must be eliminated by boundary conditions. The masses in these Yukawa potentials are only weakly constrained by the observational evidence to be $ \geq10^{-4}~cm^{-1} $. Although the magnitude of these effects is negligible at laboratory or astronomical distances, there are some interesting qualitative features.This paper discusses classical gravity theories with higher-order derivatives. Including terms like $ f_{\mu\nu}R^{\mu\nu}(-g)^{1/2} $ and $ \int R^{2}(-g)^{1/2} $ in the gravitational action leads to a class of effectively multimass gravity models. These models include, in addition to massless spin-two excitations, massive spin-two and massive scalar excitations, resulting in a total of eight degrees of freedom. The massive spin-two part of the field has negative energy. Specific ratios of the two new terms can eliminate either the massive tensor or the massive scalar, reducing the number of degrees of freedom. The static, linearized solutions of the field equations are combinations of Newtonian and Yukawa potentials. Observational evidence only weakly restricts the new masses. The acceptable static metric solutions in the full nonlinear theory are regular at the origin. The dynamical content of the linearized field is analyzed by reducing the fourth-order field equations to separated second-order equations, related by coupling to external sources in a fixed ratio. This analysis is carried out into the various helicity components using the transverse-traceless decomposition of the metric. The paper discusses the inclusion of higher-derivative terms in the gravitational Lagrangian, which stabilizes the divergence structure of gravity, allowing it to be renormalized. The early investigators thought that all classical tests of general relativity were automatically satisfied by these models. However, it was later pointed out that solutions of purely four-derivative models which do couple to a positive matter source are not asymptotically flat at infinity. The paper restricts itself to models derived from actions that include both the Hilbert action $ f(-g)^{1/2}R $ and the four-derivative terms. The action is written in the form $ I=-\int(-g)^{1/2}(\alpha R_{\mu\nu}R^{\mu\nu}-\beta R^{2}+\gamma\kappa^{-2}R) $, where $ \kappa^{2}=32\pi G $, and $ \alpha $, $ \beta $, and $ \gamma $ are dimensionless numbers. It is found that the correct physical value for $ \gamma $ is 2, as in Einstein's theory. The static spherically symmetric solutions to the field equations derived from (1.1) either reduce asymptotically to the sum of a Newtonian and two Yukawa potentials, or they are unbounded at infinity and must be eliminated by boundary conditions. The masses in these Yukawa potentials are only weakly constrained by the observational evidence to be $ \geq10^{-4}~cm^{-1} $. Although the magnitude of these effects is negligible at laboratory or astronomical distances, there are some interesting qualitative features.