In this paper we consider the following continuous Sobolev inner product on
the unit circle
<f(z), g(z)> (s) = integral (2 pi)(0)f(e(i theta))g(e(i theta))d mu(theta)
+ 1/lambda integral (2 pi)(0) f'(e(i theta))g'(e(i theta))d theta /2 pi, z
= e(i theta),
where lambda > 0, d mu(theta) is a Bernstein-Szego measure and d theta /2 p
i is the normalized Lebesgue measure on [0, 2 pi]. We study the correspondi
ng sequence of orthogonal polynomials. Algebraic properties, asymptotic beh
avior and asymptotic distribution of zeros for such polynomials are obtaine
d.