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This paper concerns criteria for assuring that every solution of a real fourth order nonselfadjoint differential equationis oscillatory at x = ∞. Our technique is a generalisation of that used by Whyburn (1) for the study of the selfadjoint equation,combined with the theory of H-oscillation of vector equations as introduced by Domšlak (2) and studied by Noussair and Swanson (3). Whyburn's technique consists of representing (1.2) as a dynamical system of the formand then studying (1.3) in terms of polar coordinates in the y, z-plane. In Section 2 below we show how to represent (1.1) as a dynamical system of the form

Generalized boundary value problems are considered for hyperbolic equations of the form utt — uss + λp(s, t)u = 0. By constructing symmetric Green's functions appropriate to such problems the existence of eigenvalues is established.