  A key aspect where extreme values methods differ from standard statistical
models is through having asymptotic theory to provide a theoretical
justification for the nature of the models used for extrapolation. In
multivariate extremes many different asymptotic theories have been proposed,
partly as a consequence of the lack of ordering property with vector random
variables. One class of multivariate models, based on conditional limit theory
as one variable becomes extreme, developed by Heffernan and Tawn (2004), has
developed wide practical usage. The underpinning value of this approach has
been supported by further theoretical characterisations of the limiting
relationships by Heffernan and Resnick (2007) and Resnick and Zeber (2014).
However Drees and Jan{\ss}en (2017) provided a number of counterexamples of
their results, which potentially undermine the trust in these statistical
methods. Here we show that in the Heffernan and Tawn (2004) framework, which
involves marginal standardisation to a common exponentially decaying tailed
marginal distribution, the problems in these examples are removed.
