In his article entitled 'Long Economic Cycles', Kondratiev argued that, in addition to the normal trade cycle of capitalism of between seven and eleven years, there existed longer cycles, the average duration of which was fifty years. He concluded that the capitalist system passes through "long waves", in which each downswing is followed by an upswing which can last for decades. It is this latter assertion that was rebutted by Trotsky. And though it has regularly made its reappearance, enjoying a temporarily fashionable status, it has no solid basis either in fact or in theory. In this article, originally published in 2000, Alan Woods explains why.