A graph is supereulerian if it has a spanning eulerian subgraph.The graphs family C(l

k) was introduced

for positive integers l and nonnegative integers k

let C(l

k) denote the family of 2-edgeconnected graphs.Graph G belongs to C(l

k) if G with order n is 2-edge-connected and for every bond E of G with two or three edges

each component of G-E has at least(n-k)/l vertices.On the basis of the case C(6

5) given

using the contraction methods

the paper proved that when G belongs to C(7

4) with F(G) less than three and under other conditions

G is supereulerian graph if and only if G cannot be contracted to any special graphs.