In this note we investigate the possibility of oscillatory behavior for a second-order selfadjoint elliptic operators on noncompact Riemannian manifolds (M, g). Let A be such an operator which is semibounded below and symmetric on C 0 ∞ ( M ) ⊆ L 2 ( M , d μ ) C_0^\infty (M)\, \subseteq \,{L^2}(M,\,d\mu ) where d μ d\mu is a volume element on M. If φ \varphi is a C ∞ {C^\infty } function such that A φ = λ φ A\varphi \, = \,\lambda \varphi , we would naively say that φ \varphi is oscillatory (and by extension λ \lambda is oscillatory if it possesses such an eigenfunction φ \varphi ) if M − φ − 1 ( 0 ) M\, - \,{\varphi ^{ - 1}}(0) has an infinite number of bounded connected components. For technical reasons this is not quite adequate for a definition. However, in §1 we give the usual definition of oscillatory which is a slight generalization of the one above. Let Λ 0 {\Lambda _0} be the number below which this phenomenon cannot occur; Λ 0 {\Lambda _0} is the oscillatory constant for the operator A. In that A is semibounded and symmetric on C 0 ∞ ( M ) ⊆ L 2 ( M , d μ ) C_0^\infty (M)\, \subseteq \,{L^2}(M,\,d\mu ) , A has a Friedrichs extension. Let Λ c {\Lambda _c} be the bottom of the continuous spectrum of the Friedrichs extension of A. Our main result is Λ 0 = Λ c {\Lambda _0}\, = \,{\Lambda _c} .