Abstract: The biomathematical theory on cyanobacteria blooming has been posed first time.Using an expansion of the exponential and logistic equations,under conditions of the blooming and the strong persistence,the laws of the population of cyanobacteria have been derived.The differential equations to describe the population of cyanobacteria under the control of the envirnmental factors phosphorus and nitrogen has been established and two theorems about the conditions of weak persistence and extinction have been proven.On the basis of the theory,the methods and ways how control the bloom and extinction of cyanobacteria are posed.