The paper by K. S. Stelle explores the inclusion of four-derivative terms, such as \( f R_{\mu \nu} R^{\mu \nu}(-g)^{1/2} \) and \( f R^2(-g)^{1/2} \), into the gravitational action, leading to a class of effectively multimass models of gravity. These models introduce massive spin-two and scalar excitations, resulting in a total of eight degrees of freedom. The massive spin-two part has negative energy, and specific ratios of the four-derivative terms can eliminate either the massive tensor or scalar excitations, reducing the degrees of freedom. The static, linearized solutions are combinations of Newtonian and Yukawa potentials, with observational evidence providing only weak constraints on the new masses. The acceptable static metric solutions in the full nonlinear theory are regular at the origin. The paper also analyzes the dynamical content of the linearized field by reducing the fourth-order field equations to second-order equations, using the transverse-traceless decomposition of the metric. The author emphasizes that the Schwarzschild solution, while a solution to the empty space equations, does not couple to a positive definite matter distribution and is thus ruled out. The paper concludes by discussing the physical implications and qualitative features of these higher-derivative models.The paper by K. S. Stelle explores the inclusion of four-derivative terms, such as \( f R_{\mu \nu} R^{\mu \nu}(-g)^{1/2} \) and \( f R^2(-g)^{1/2} \), into the gravitational action, leading to a class of effectively multimass models of gravity. These models introduce massive spin-two and scalar excitations, resulting in a total of eight degrees of freedom. The massive spin-two part has negative energy, and specific ratios of the four-derivative terms can eliminate either the massive tensor or scalar excitations, reducing the degrees of freedom. The static, linearized solutions are combinations of Newtonian and Yukawa potentials, with observational evidence providing only weak constraints on the new masses. The acceptable static metric solutions in the full nonlinear theory are regular at the origin. The paper also analyzes the dynamical content of the linearized field by reducing the fourth-order field equations to second-order equations, using the transverse-traceless decomposition of the metric. The author emphasizes that the Schwarzschild solution, while a solution to the empty space equations, does not couple to a positive definite matter distribution and is thus ruled out. The paper concludes by discussing the physical implications and qualitative features of these higher-derivative models.