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We study gravitational perturbations in the Randall-Sundrum two-brane background with scalar-curvature terms in the action for the branes, allowing for positive as well as negative bulk gravitational constant. In the zero-mode approximation, we derive the linearized gravitational equations, which have the same form as in the original Randall-Sundrum model but with different expressions for the effective physical constants. We develop a generic method for finding tachyonic modes in the theory,doi:10.1088/0264-9381/22/6/007 fatcat:7eizro2bojhapnj2accrycsctu