In this study a discontinuous boundary value problem with retarded argument and with transmission conditions at the point of discontinuity are investigated. In the special case that our problem is continuous (i. e. when delta = 1 in below) the obtained results coincidewith corresponding results in [S. B. Norkin, On boundary problem of Sturm-Liouville type for second-order differential equation with retarded argument, Izv. Vyss . Ucebn. Zaved. Matematika 6 (7) (1958) 203-214]. (c) 2007 Elsevier Inc. All rights reserved.