Abstract. As a model for an interface in solid state physics, we consider two real-valued potentials V (1) and V (2) on the cylinder or tube S = R × (R/Z) where we assume that there exists an interval (a 0 , b 0 ) which is free of spectrum of −∆ + V (k) for k = 1, 2. We are then interested in the spectrum of Ht = −∆ + Vt, for t ∈ R, where Vt(x, y) = V (1) (x, y), for x > 0, and Vt(x, y) = V (2) (x + t, y), for x < 0. While the essential spectrum of Ht is independent of t, we show that discrete spectrum, related to the interface at x = 0, is created in the interval (a 0 , b 0 ) at suitable values of the parameter t, provided −∆ + V (2) has some essential spectrum in (−∞, a 0 ]. We do not require V (1) or V (2) to be periodic. We furthermore show that the discrete eigenvalues of Ht are Lipschitz continuous functions of t if the potential V (2) is locally of bounded variation.