The authors consider the following system of delay differential equations which describe the delayed predator-prey system \[ \begin{aligned}\dot{x}(t) & = x(t)[ r_1 - a_{11} x(t-\tau) - a_{12}y(t-\tau) ] ,\\ \dot{y}(t) & = y(t)[-r_2 +a_{21}x(t-\tau) - a_{22}y(t-\tau)], \end{aligned} \] where the scalar variables \(x\) and \(y\) can be interpreted as population densities of prey and predator, \(\tau>\) is the feedback time delay, \(r_1\) is the intrinsic growth rate of the prey and \(r_2\) denotes the death rate of the predator. The main results include the stability analysis of the zero equilibrium, conditions for Hopf bifurcations, direction of the Hopf bifurcations and analysis of the stability of the bifurcating periodic solutions.