In this paper we firstly introduce the concept of a normal system in an orthogroup and the concept of the kernel system of a homomorphism of an orthogroup. The normal systems in an orthogroup are completely determined. In the latter half of the paper, some generalizations of results appear in the group theory are established for orthogroups by using the above-mentioned concepts instead of the concepts of a normal subgroup and the kernel of a homomorphism in the group theory. The complete proofs are almost omitted, and only an outline of the results is given.