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The authors consider operators of the form $L=sum_{i=1}^X_^+X_$ in a bounded domain of $mathbb^$ where $X_,X_,ldots,X_$ are nonsmooth Hormander's vector fields of step $r$ such that the highest order commutators are only Holder continuous. Applying Levi's parametrix method the authors construct a local fundamental solution $gamma$ for $L$ and provide growth estimates for $gamma$ and its first derivatives with respect to the vector fields. Requiring the existence of one more derivative of the coefficients the authors prove that $gamma$ also possesses second...