A general scaling theory of transient phenomena is formulated near the instability point for the moments of the relevant intensive macrovariable, for the generating function, and for the probability distribution function. This scaling theory is based on a generalized scale transformation of time. The whole range of time is divided into three regions, namely the initial, scaling, and final regions. The connection procedure between the initial region and the scaling region is studied in detail. This scaling treatment has overcome the difficulty of divergence of the variance for a large time which was encountered in the -expansion, and this scaling theory yields correct values of moments to order unity for an infinite time. Some instructive examples are discussed for the purpose of clarifying the concepts of the scaling theory.