Generalized Parton Distributions for large $x$

The $t$-dependence of generalized parton distrbutions for $x\to 1$ is discussed. We argue that constituent quark models, where the $t$-dependence for $x\to 1$ is through the product $(1-x)t$, are inconsistent. Instead we suggest a leading dependence in terms of $(1-x)^n t$, where $n\geq 2$, for $x\to 1$.