Let be a finite positive Borel measure supported on [−1, 1] and introduce the discrete Sobolev-type inner productwhere the mass points a k belong to [−1, 1], and M k,i > 0(i = 0, 1, . . . , N k ). In this paper, we obtain generalized trace formula and asymptotics of the averaged Turan determinant for the Sobolev-type orthogonal polynomials. Asymptotics of the recurrence coefficients for symmetric Gegenbauer-Sobolev orthogonal polynomials is obtained. Trace formula and asymptotics of Turan's determinant for Gegenbauer-Sobolev orthogonal polynomials are also given.