The subject of the special functions of the single complex variable and several complex variables occupies a great attention in almost all disciplines Mathematics, Physics and Engineering. The present work is devoted to study this subject, taking it into account as one of several theses, which presented and still being presented by Specialists in complex analysis. The main aim of this thesis defining and studying of some special functions which contain two complex variables such as Bessel matrix function, Tricomi matrix function, Horn matrix function and Struve matrix function and also providing special inequalities of Bessel functions and modified Bessel functions and Tricomi functions of two scalar index of two complex variables and of their ratios.