The authors consider the nonlinear differential-difference equation
where are positive constants, , and is continuously differentiable. First, the local stability of the zero solution to (1) is investigated. Second, it is shown that the two delay equation exhibits Hopf bifurcation and that the Hopf bifurcation is supercritical and the bifurcating periodic solutions are orbitally stable under certain conditions. Results of the paper improve some of the results obtained by J. Bélair and S. A. Campbell [SIAM J. Appl. Math. 54, No. 5, 1402-1424 (1994; Zbl 0809.34077)].