Recently ,a lot of coding scholars show a great interest in the study of constacyclic codes and constacyclic self-du-al codes over the residue rings .In this paper ,by utilizing some related linear codes ,we first give the general theory of constacyclic self-dual codes of length N over a class of special finite chain rings .Using the obtained results ,we give the sufficient conditions of the existence of constacyclic self-dual codes of length N over the ring .Finally ,we determine the structures of some constacyclic self-dual codes of length N over the ring and give their generator polynomials .%最近，剩余类环上的常循环码及常循环自对偶码引起了编码学者的极大关注。本文首先利用一些相关的线性码，建立了一类特殊有限链环上长为 N的常循环自对偶码的一般理论，利用其结果给出了该环上长为 N的（1＋ uλ）-常循环自对偶码存在的充分条件，得到了该环上长为 N的一些常循环自对偶码，并给出了其生成多项式。
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