In 1958 Obrechkoff [1] Introduced a generalization or the integral transforms of Laplace and Meijer. In the same paper some differential and asymptotic properties of its kernel function were investigated and a real inversion formula of the Post-Widder type was found. Later on, Dimovski [2, 3] proposed a modification of this transform, usually referred to as the Obrechkoff integral transform. As was shown in [2-5], it can be used as a basis or an operational calculus for the most general Bessel type differential operator of an arbitrary order. It has turned out that a number of Bessel type integral transformations proposed by different authors ore quite special cases of the Obrechkoff transform. Here, we shall propose Abelian theorems for this transform, that is "initial (final) value" theorems relating the initial (final) value of an original to the final (initial) value of its transformation.