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Recently, infinite and finite dimensional generalized Hilbert tensors have been introduced. In this paper, the authors further introduce infinite and finite dimensional generalized Cesaro tensors as a generalization of Cesaro matrices and discuss the properties of these structured tensors. Next, some  upper bounds of $Z_{1}$-spectral radius of generalized Cesaro tensors  and  generalized Hilbert tensors are given,  which improves the existing ones. Finally, we obtain conditions under which a generalized Cesaro tensor is column sufficient tensor.