In this paper, we study homomorphism theorems in ordered semirings by using pseudoorder. Pseudoorder in ordered semirings has been defined and the construction of a pseudoorder on a semiring induced by homomorphisms of ordered semirings has been given. In the other way, homomorphism theorems of ordered semirings by using compatible quasiorder has been introduced. However, we can show that compatible quasiorder is not equal to pseudoorder. Finally, we prove the homomorphism theorems in ordered semirings by using pseudoorder to complete the study of ordered semirings based on pseudoorder.