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For a graph G and even integers b a 2, a spanning subgraph F of G such that a deg F (x) b and deg F (x) is even for all x ∈ V (F) is called an even [a, b]-factor of G. In this paper, we show that a 2-edge-connected graph G of order n has an even [2, b]-factor if max{deg G (x), deg G (y)} max 2n 2+b , 3 for any nonadjacent vertices x and y of G. Moreover, we show that for b 3a and a > 2, there exists an infinite family of 2-edge-connected graphs G of order n with δ(G) a such that G satisfies the condition deg G (x) + deg G (y) > 2an a+b for any nonadjacent vertices x and y of G, but has no even [a, b]-factors. In particular, the infinite family of graphs gives a counterexample to the conjecture of Matsuda on the existence of an even [a, b]-factor.