Multivariate extreme value models and associated statistical methods a
re developed for vector observations whose components are subject to a
n order restriction. The approach extends the multivariate threshold m
ethodology of Coles and Tawn, Joe and co-workers and Smith and cc-work
ers. The results are illustrated by an analysis of extreme rainfalls o
f different durations, and by a study of the problem of linking a long
series of daily rainfall extremes with a partially overlapping shorte
r series of hourly extremes.