  A clone on a set X is a set of finitary functions on X which contains the
projections and which is closed under composition. The set of all clones on X
forms a complete algebraic lattice Cl(X). We obtain several results on the
structure of Cl(X) for infinite X. In the first chapter we prove the
combinatorial result that if X is linearly ordered, then the median functions
of different arity defined by that order all generate the same clone. The
second chapter deals with clones containing the almost unary functions, that
is, all functions whose value is determined by one of its variables up to a
small set. We show that on X of regular cardinality, the set of such clones is
always a countably infinite descending chain. The third chapter generalizes a
result due to L. Heindorf from the countable to all uncountable X of regular
cardinality, resulting in an explicit list of all clones containing the
permutations but not all unary functions of X. Moreover, all maximal submonoids
of the full transformation monoid which contain the permutations of X are
determined, on all infinite X; this is an extension of a theorem by G. Gavrilov
for countable base sets.
