In this paper first we give some definitions and

examples on hyper$K$-algebras. Then we give some theorems and

obtain some results which are needed to state and prove the main

theorems of this manuscript (Theorems 3.16 and 3.21). In these

theorems we give some classifications of hyper$K$-algebras of

order 3 which satisfy the normal condition or simple

condition. Finally we give two open problems.