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The stability of cyclical growth within the context of a model in “Growing through cycles” in Econometrica by Matsuyama (1999) is examined. It is shown that but for an extreme situation, the two‐period cycles (two‐cycles) are unique and a range of parameter values that imply the stability of such cyclical growth is derived. The growth enhancing property of two‐cycles are shown to be retained by any cycle; the results of simulation exercises carried out are reported to show that for a very wide range of parameter values, such cyclical growth paths are stable and, therefore, robustness of the conclusions is established.