Abstract: We consider generalized Schroedinger operators with an attractive delta-type interaction supported by an infinite curve with no cusps and self-intersections which is asymptotically straight in a suitable sense. We show that unless the curve is a straight line, the operator has at least one isolated eigenvalues below the threshold of the essential spectrum. For more details see P. Exner and T. Ichinose, J. Phys. A34 (2001), 1439-1450, and also math-ph/0001015.