We propose a method for defining and measuring spatial contagion between two financial markets via conditional copulas. Some theoretical results on monotonicity and asymptotic properties of Gaussian copulas with respect to conditioning are presented. Next, we combine the spatial contagion approach with time series models. We investigate which model from a large family of multivariate GARCH is the best tool for modelling spatial contagion. In an empirical study, we show that among models designed for general fit, a two-step model fitting procedure reduces the ability to describe the contagion effect. This is a feature of copula-GARCH models. Copyright © 2013 John Wiley & Sons, Ltd.