In a recent work by the present authors, an analytical kinetic model has been derived for solid-state phase transformations on the basis of summation/product transition. In the present paper, this approach is extended to models that describe transformations involving various time synchronous and time asynchronous sub-processes. According to the newly proposed models, several interesting kinetic phenomena are revealed: negative sub-processes are responsible for the decreasing tendency of Avrami exponent; the evolution of overall kinetic parameters during time synchronous transformation reflects the relative contributions from different sub-processes; the mechanism of transformation subject to Avrami nucleation can be regarded as a combination of various time synchronous sub-processes; a process due to continuous nucleation is equal to the total effect of infinitely many sub-processes due to site saturation starting at different times; and abnormal results of Avrami plot in time asynchronous transformation are due to a sudden change in transformation mechanisms. Finally, the time asynchronous model is applied successfully to describe the crystallizations of Mg-Cu-Y and Zr-Cu-Al amorphous alloys, measured by differential scanning calorimetry.