To provide an accessory for an exterior wall, which is excellent in general-purpose properties because it can hold a plurality of downpipes, and an accessory set for the exterior wall, which is equipped with the accessory.

A long and approximately recessed cross-section downpipe storage portion 9, which is arranged in a vertical groove portion 5 opened on an outdoor side and formed in the exterior wall 3 of a building, is provided. Downpipe holding portions 11, which hold the downpipe 4 by abutting on the outer surface of the downpipe 4 housed in the downpipe storage portion 9, are formed on both the side piece portions 14 of the downpipe storage portion 9, respectively. Each of the downpipe holding portions 11 is formed in a cross-sectional arc shape convex toward the width-direction outside of the downpipe storage portion 9; and both side portions of an arc are composed of elastic piece portions 16, respectively.