In the last few years there has been considerable research on differen
tial algebraic equations (DAEs) f(x', x, t) = 0, where f(x') is identi
cally singular. The index provides one measure of the singularity of a
DAE. Most of the numerical analysis literature on DAEs to date has de
alt with DAEs with indices no larger than three, because of technical
difficulties and because many basic applications including constrained
mechanical systems have this index. This paper discusses several situ
ations where DAEs of index higher than three occur naturally. It will
also discuss the relationship between certain concepts in nonlinear co
ntrol theory such as relative degree and zero dynamics, the index, and
constrained mechanical systems.