Creative destruction due to new technologies causes both long-run growth and short-run business fluctuations. The creative part of new technologies pushes the economy on a higher productivity level while the destructive part implies partial obsolescence of old production units. Obsolescence due to each new technology induces an adjustment period during which growth rates are initially high but gradually fall. At some endogenously determined point, research for the next technology starts. Once the new technology is discovered, the next cycle starts. This is shown in a continuous time Ramsey growth model where savings can be used for financing deterministic capital accumulation and stochastic Poisson driven R&D for new technologies.