Attempts were made to derive more flexible growth models to describe an indeterminate growth process such as stem d. b. h. First, we show that the GOMPERTZ and Logistic functions, in addition to the MITSCHERLICH function, are derived identically by using the differ-ence equation of the first order in which variables in the time series data are transformed into logarithms or reciprocals. Second, growth functions of polyno-mial form corresponding to the primary functions are derived by handling mathe-matically the difference equation of the second order as extended growth models. Then, for two of these functions, the MITSCHERLICH type and the GOMPERTZ type, their fitting method and fitness are explored experimentally for d. b. h. growth data at intervals of 5 years from stem analysis of Japanese larch (Larix leptolepis GORD.) and todo-fir (Abies sachalinensis MAST.). The results demon-strate that the proposed growth functions provide the possibility of describing any growth processes which change their asymptotic values for other ones on their way to final size.