This paper is concerned with two$n$-species stochastic cooperative systems. One is autonomous, theother is non-autonomous. For the first system, we prove that foreach species, there is a constant which can be represented by thecoefficients of the system. If the constant is negative, then thecorresponding species will go to extinction with probability 1; Ifthe constant is positive, then the corresponding species will bepersistent with probability 1. For the second system, sufficientconditions for stochastic permanence and global attractivity areestablished. In addition, the upper- and lower-growth rates of thepositive solution are investigated. Our results reveal that,firstly, the stochastic noise of one population is unfavorable forthe persistence of all species; secondly, a population could bepersistent even the growth rate of this population is less than thehalf of the intensity of the white noise.