Abstract.Let dv be a nonnegative Borel measure on \-n, n], with 0 < f*n du < co and with support of Lebesgue measure zero. We show that there exist {Vj}%¡ C (0, oo) and {tj}jZ\ C (-it, n) such that if 00 dß(6) :=Y/1jdu(d + tj), 6 e[-n , ti], j=i (with the usual periodic extension dv(d ± 2n) = dv(6)), then the leading coefficients {Kn(dß)}^L0 of the orthonormal polynomials for dß satisfy \im>K"(dp)/Kn+x(dp)= 1.As a consequence, we obtain pure singularly continuous measures da on [-1,1] lying in Nevai's class M .