Abstract: The present paper presents the decomposition theorems for near rings satisfying any one of the conditions: (1) xy=y^{m(xypyn; (2) xy=ym(yx)pyn, where m=m(x,y)≥0, n=n(x,y)≥0 and p=p(x,y)>1 are integers.}

Key words: distributively generated (d-g)-near ring, D-near ring, zero-symmetric near ring, zero-commutative near ring