In this note we demonstrate that in affine models for bilateral exchange rates, the nature of return interdependence during crises depends on the tail properties of the fundamentals' distributions. We denote crisis linkages as either strong or weak, in the sense that the dependence remains or vanishes asymptotically. We show that if one currency return reaches crisis levels, the probability that the other currency breaks down as well vanishes asymptotically if the fundamentals' distributions exhibit light tails (like e.g. the normal). However, if the marginal distributions exhibit heavy tails, the probability that the other currency breaks down as well remains strictly positive even in the limit. This result implies that linearity and heavy tails are sufficient conditions for joint or contagious currency crises to happen systematically through fundamentals.