The object of the present paper is to investigate several classes of analytic functions with varying argument of coefficients, which are defined here by means of the principle of subordination between analytic functions. Such properties as the coefficient estimates, distortion theorems, subordination theorems, convolution properties, integral means inequalities, and radii of convexity and starlikenes are investigated. Some consequences of our main results for new or known classes of analytic functions are also pointed out.