The cycle embedding problem in 3 ary n cubes with conditional fault edges was discussed.It is proved that each vertex is incident to at least two healthy edges for those cubes of n≥2 and there exists a cycle with its length from 3 to 3n in a 3 ary n cube if the number of fault edges are less than 2n-1 and the subgraph induced by the fault edges is acyclic.