The distance matrix of a simple connected graph G is D(G) = (dij), where dij is the distance between the ith and jth vertices of G. The distance signless Laplacian matrix of the graph G is DQ(G) = D(G) + Tr(G), where Tr(G) is a diagonal matrix whose ith diagonal entry is the transmission of the vertex i in G. In this paper, first, upper and lower bounds for the spectral radius of a nonnegative matrix are constructed. Applying this result, upper and lower bounds for the distance and distance signless Laplacian spectral radius of graphs are given, and the extremal graphs for these bounds are obtained. Also, upper bounds for the modulus of all distance (respectively, distance signless Laplacian) eigenvalues other than the distance (respectively, distance signless Laplacian) spectral radius of graphs are given. These bounds are probably first of their kind as the authors do not find in the literature any bound for these eigenvalues. Finally, for some classes of graphs, it is shown that all distance (respectively, distance signless Laplacian) eigenvalues other than the distance (respectively, distance signless Laplacian) spectral radius lie in the smallest Gerŝgorin disc of the distance (respectively, distance signless Laplacian) matrix.