Let G be a d-regular multigraph, and let λ 2 (G) be the second largest eigenvalue of G. In this paper, we prove that if, then G is 2-edgeconnected. Furthermore, for t ≥ 2 we show that G is (t + 1)-edge-connected when λ 2 (G) < d − t, and in fact when λ 2 (G) < d − t + 1 if t is odd.