In this paper we propose a new framework for modelling heteroskedastic structural vector autoregressions. The identification of the structural parameters is obtained by exploiting the heteroskedasticity in the data naturally arising during crisis periods. More precisely, we provide identification conditions when heteroskedasticity and traditional restrictions on the parameters are jointly considered. Although the framework is general enough to find potential applications in many empirical economic fields, it proves to be well suited for distinguishing between interdependence and contagion in the literature related to the transmission of financial crises. This methodology is used to investigate the relationships between sovereign bond yields for some highly indebted EU countries.