The author formulates and proves three theorems for the Lipschitz stability of systems of nonlinear differential equations. First, the uniformly stable zero solution is stated. Then under some conditions the uniform Lyapunov stability for the zero solution is proved. Introducing an additional function allows the author to consider a single equation for this function. The equivalence of the uniform Lipschitz stability of the zero solution to this equation and to the primitive system is established. A system of two ordinary differential equations is presented as example.