  Conditionally specified models are often used to describe complex
multivariate data. Such models assume implicit structures on the extremes. So
far, no methodology exists for calculating extremal characteristics of
conditional models since the copula and marginals are not expressed in closed
forms. We consider bivariate conditional models that specify the distribution
of $X$ and the distribution of $Y$ conditional on $X$. We provide tools to
quantify implicit assumptions on the extremes of this class of models. In
particular, these tools allow us to approximate the distribution of the tail of
$Y$ and the coefficient of asymptotic independence $\eta$ in closed forms. We
apply these methods to a widely used conditional model for wave height and wave
period. Moreover, we introduce a new condition on the parameter space for the
conditional extremes model of Heffernan and Tawn (2004), and prove that the
conditional extremes model does not capture $\eta$, when $\eta<1$.
