Let λ 1 (G) and q 1 (G) be the spectral radius and the signless Laplacian spectral radius of a k-uniform hypergraph G, respectively. In this paper, we give the lower bounds of d − λ 1 (H) and 2d − q 1 (H), where H is a proper subgraph of a f (edge)-connected d-regular (linear) k-uniform hypergraph. Meanwhile, we also give the lower bounds of 2∆ − q 1 (G) and ∆ − λ 1 (G), where G is a nonregular f (edge)-connected (linear) k-uniform hypergraph with maximum degree ∆