This paper studies the stability of the M1 and M2 money demand function in Malaysia. The results showed that both M1 and M2 are cointegrated with their determinants. However, only the long-run parameter of M1 demand function is stable over the sample period, not M2. The demand function became unstable after 1997 which coincided with the Asian financial crisis. This result contradicts that of Nair et al (2008) who claims that the Asian financial crisis does not have any influence on the stability of money demand function in Malaysia. Out finding also implied that a simple relationship between M2, income and interest rates characterized by the standard model is not sufficient to analyze the effects of Malaysian monetary policy.