  The class of linearly ordered sets with one order preserving unary operation
has the Strong Amalgamation Property (SAP). The class of linearly ordered sets
with one strict order preserving unary operation has AP but not SAP. The class
of linearly ordered sets with two order preserving unary operations has not AP.
For every set $F$, the class of linearly ordered sets with an $F$-indexed
family of automorphisms has SAP. Corresponding results are proved in the case
of order reversing operations. Various subclasses of the above classes are
considered and some model-theoretical consequences are presented.
