The codes of formal power series rings R_{\infty}=\mathbb{F}[[\gamma]]=\Sigma_{l=0}^{\infty}a_{l}\gamma_{l}|a_{l}\in\mathbb{F}}  and finite chain rings 

Ri={a0+a1r+…+ai-1\gamma^i-1|ai∈\mathbb{F}} have close relationship in lifts and projection. In this paper, we study self-dual codes over R∞ by means of self-dual codes over Ri,  and give some characterizations of self-dual codes over R∞.