Generalized amalgamation and -simplicity

We study generalized amalgamation properties in simple theories. We formulate a notion of generalized amalgamation in such a way so that the properties are preserved when we pass from T to T e q or T h e q ; we provide several equivalent ways of formulating the notion of generalized amalgamation. ine two distinct hierarchies of simple theories characterized by their amalgamation properties; examples are given to show the difference between the hierarchies.