We study heteroclinic orbits and transition motions in a class of conservative systems. The unperturbed systems are assumed to have two nonhyperbolic equilibria connected by a heteroclinic orbit on each level set of conservative quantities. We restrict ourselves to the case in which the perturbations contain single frequency components. These equilibria construct two normally hyperbolic invariant manifolds in the unperturbed phase space, and by the invariant manifold theory there exist two normally hyperbolic, locally invariant manifolds in the perturbed phase space. We extend Melnikov's method to give a condition under which the stable and unstable manifolds of these locally invariant manifolds intersect transversely. Moreover, when the locally invariant manifolds consist of closed orbits, we show that the closed orbits near the unperturbed equilibria on different level sets can be connected by heteroclinic orbits and there can exist transition motions from a neighborhood of the unperturbed equilibrium on a level set to that of one on a different level set. This behavior can occur even when the two unperturbed equilibria on each level set coincide and have a homoclinic orbit. We illustrate our theory for the rigid body with a flywheel attachment.