In this paper, the asymptotic expression of the eigenvalues and eigenfunctions of the Sturm-Liouville equation with the lag argument y''(t) + l2 y(t) + M(t)y (t - D(t)) = 0 and the spectral parameter in the boundary conditions l y(0) +y'(0) = 0 l2y(p) + y'(p) = 0 y(t - D(t)) = y(0)j(t - D(t)), t - D(t) < 0 has been founded in a finite interval, where M(t) and D(t) \geq 0 are continuous functions on [0, p], l > 0 is a real parameter, j(t) is an initial function which is satisfied with the condition j(0) = 1 and continuous in the initial set.

In this paper, the asymptotic expression of the eigenvalues and eigenfunctions of the Sturm-Liouville equation with the lag argument y''(t) + l2 y(t) + M(t)y (t - D(t)) = 0 and the spectral parameter in the boundary conditions l y(0) +y'(0) = 0 l2y(p) + y'(p) = 0 y(t - D(t)) = y(0)j(t - D(t)), t - D(t) < 0 has been founded in a finite interval, where M(t) and D(t) \geq 0 are continuous functions on [0, p], l > 0 is a real parameter, j(t) is an initial function which is satisfied with the condition j(0) = 1 and continuous in the initial set.