In this paper, we develop a business cycle model with general investment, variable depreciation rate of capital stock and two delays. The first delay describes the time lag between the decision of investment and its implementation, while the second one models the time lag for investment to be produced. The well-posedness and the existence of economic equilibrium are carefully investigated. Moreover, the stability of the economic equilibrium and the existence of Hopf bifurcation are established. The case when the two delays are equal is rigourously studied.