This paper proposes a definition of bivariate and multivariate co-movement and an associated measure that precisely reflects its definition. It is shown that co-movement as defined in this paper is a copula property. We employ a truly multivariate and dynamic analysis and analyze whether co-movements have increased through time, in crisis periods and whether there are differences between normal and extreme co-movements. Empirical results for different portfolios of monthly stock market returns generally show that positive and negative co-movements have increased in recent years. However, in crisis periods co-movements have not always increased. Furthermore, while normal co-movements have increased for all portfolios, extreme co-movements have increased for some markets but not for all. Finally, the results clarify that the multinomial logit model used to estimate the probability of co-movement can be viewed as an alternative to Multivariate GARCH models.