We construct graphs that are cospectral but nonisomorphic with Kneser graphs K(n, k), when n =3k - 1, k> 2 and for infinitely many other pairs (n, k). We also prove that for 3 ≤ k ≤ n - 3 the Modulo-2 Kneser graph K2(n, k) is not determined by the spectrum