Problems of stream order and distnbution of stream number in stream network systems were studied by starting from the basic postulate of the statistical theory that natural stream network systems in the absence of strong geologic controls are very nearly topologically random.
First, the occurrence probability of maximum order in stream network systems by Strahler ordering was computed for given number of first-order streams. The results were shown that the occurrence probability of maximum order by Strahler ordering can be expressed by means of formula for lognormal probability density function.
Also, the approximate formulas for the relations between basin area and maximum stream order in stream network systems were obtained by using the result of statistical theory in stream network systems and the value of first-order stream number perunit area.
Second the occurrence probability of stream number for each order in stream network systems ordering by Strahler method was given by the simple recurrent formula. Moreover, the calculations were carried out by this recurrent formula and it was found that the distribution of Strahler stream number drawn from an infinite topologically random stream network systems is approximately given by the normal probability density function.