Abstract: For a proper total coloring of a graph G=(V,E), thepalette C(v) of a vertex v\in V is the set of the colors of the
edges incident with v and the color of the vertex itself. If C(u)\neq C(v), then the two vertices u and v of G are said to be distinguished by the total coloring. A d-strong total coloring of G is a proper total coloring that distinguishes all pairs of verticeu and vwith distance 1\leq d_{G}(u,v)\leq
d. The d-strong total chromatic number chi^{''}_{d}(G) of Gis the minimum number of colors of a d-strong total coloring ofG. In this paper we determine \chi^{''}_{d}(C_{n}) completely for cycles where d\in [35,55]$ and $d\in \textbf{N