We investigate the spectral types of unitary operator U on L2(T) defined by (Uf)(x) = A(x)f(x + theta), \A(x)\ = 1 a.e., where T is the unit circle identified with the half open interval [0, 1) and theta is irrational. It is shown that Veech's result on the Kronecker-Weyl theorem modulo 2 is closely related to the spectral type of U.