This paper investigates the existence of non-linear dependence in Portuguese financial time series namely stock exchange indexes returns. Non-linear dependence may exist in a series even if we have already concluded for the lack of linear dependence. If present, non-linear dependence would contradict the random walk model and the financial markets weak form efficiency hypothesis. Using daily observations for the period 1990-1997 some so-called non-linearity tests are performed in order to decide whether we can accept the weak form efficiency hypothesis. The results seem to confirm the existence of exploitable excess profit opportunities in the Portuguese stock market.