Following the pattern of the theory of modules over rings BERTHMUME [l] introduced as a generalization the concepts of injective and weakly injective S-systems and proved the existence of such S-systems. There are two more weaker forms hf injectivity called quasi-injectivitg [2] and divisibility. I n this paper we shall study the relation between thosc concepts. I n [l] &n example is given showing that weakly injective S-systcins need not be injective. S o w we shall provide examples of quasi-injective-systems and divisible systems which are not weakly injective. Also there exist examples of S-systems which are not weakly injective even though every one of its proper subsystems are weakly injective. I n 1.2, 1.3 and 1.4 we show that S-systems over certain class of semigroups are weakly injective if every proper subsystem is weakly injective. The second part of the first section degcribes the structure of endomorphism semigroups of quasiinjective systems. I n the second section we find conditions when a semigroup considered as an 8-system over itself is quasi-injective and weakly injective and describe some properties of quasi-injeotivo semigroups. I n the last section we shall define divisible systems similar to the concept of divisible modules and observe various conditions when divisible systems are weakly injective and vice versa.