Filters having a high accuracy, small pressure loss, and long filtration life compared with conventional filters are provided. The filters are composed of non-woven fibrous agglomerates and are constructed in such a way that at least two layers of a non-woven fibrous agglomerate of a pre-filtration layer and a precision filtration layer are disposed therein; the pre-filtration layer is constructed in such a way that the diameter of the fibers in the pre-filtration layer becomes gradually smaller toward the direction of filtration; and at least 10% by weight of the fibers in the precision filtration layer are fibers having a diameter smaller than that of the fibers having a smallest diameter in the pre-filtration layer.