In this paper we calculate presentations for some natural monoids of transformations on a chain X n = 1 < 2 < · · · < n . First we consider n [ n ], the monoid of all full [partial] transformations on X n that preserve or reverse the order. Two other monoids of partial transformations on X n we look at are n and n -the elements of the first preserve the orientation and the elements of the second preserve or reverse the orientation.