With a generalized version of the endogenous growth model by Romer in [20] it is analysed the dynamical characteristics of the effects of the learning-by-doing (LBD) externalities on the memory-dependent production process. It is regarded as an quasi-homogeneous production function whose factors of substitutability are non-constant. It is assumed that the consumer maximizes the utility of consumption according to a constant relative risk-aversion function. The functional forms for the optimal capital formation trajectory and externalities with two-delayed arguments are solutions obtained by optimality principle. The optimal problem admits a steady state. Taking consumption elasticity as a function of one of the delays, we observe economic fluctuations which can be attenuated by the actions of both the delay effect and damping. But, there is a critical value for consumption elasticity at which economic fluctuations become unstable.