Summary: We prove that the weighted differences of ergodic averages, induced by a Cesàro bounded, strongly continuous, one-parameter group of positive, invertible, linear operators on \(L^{p}\), \(1 < p < {\infty}\), converge almost every where and in the \(L^{p}\)-norm. We obtain first the boundedness of the ergodic maximal operator and the convergence of the averages.