I have been studying ordinary differential equations in the complex domain. Topics treated are series expansions of solutions around singularities, asymptotics of hypergeometric functions of several variables, and meromorphic solutions of nonlinear differential equations e.g. Painlevé equations. These differential equations define special functions. Noticing this fact, I have examined these special functions through the corresponding differential equations. In treating these equations, complex analysis is an important tool. In particular, recently I am interested in value distribution theory and I am studying the value distribution of Painlevé transcendents. Concerning the global properties of Painlevé equations, there are many interesting results (P. Boutroux, R. Garnier, H. Wittich ...). However, some of these results are incomplete or have not been justified. For example, concerning the growth order of Painlevé transcendents, P. Boutroux (around 1910), H. Wittich and E. Hille (around 1950) gave some estimates whose proofs contain theoretical gaps caused by the difficulty in treating higher order equations. Recently I have succeeded in estimating the growth order rigorously. Hereafter I would like to study analytic and global properties of nonlinear equations (containing partial equations) using complex analysis, isomonodromic deformation and so on.