This paper is a continuation of "Homotopy Associativity of H-spaces. I" by James Dillon Stasheff. It delves deeper into the study of homotopy associativity from the perspective of homotopy theory, focusing on associative H-spaces and homotopy associative H-spaces. The author introduces the tilde construction, a generalization of the bar construction, and discusses its spectral sequence. The paper also explores Yessam operations in homology, which are similar to Massey operations in cohomology but are independent of them. Additionally, it defines and analyzes $A_n$-maps, which are special types of maps between associative H-spaces, and their relationship to the Dold and Lashof construction. The paper applies these concepts to Postnikov systems of $A_n$-spaces, particularly those with just two nontrivial homotopy groups. Finally, it examines the obstruction theory for $A_n$-maps and the classification of loop classes.This paper is a continuation of "Homotopy Associativity of H-spaces. I" by James Dillon Stasheff. It delves deeper into the study of homotopy associativity from the perspective of homotopy theory, focusing on associative H-spaces and homotopy associative H-spaces. The author introduces the tilde construction, a generalization of the bar construction, and discusses its spectral sequence. The paper also explores Yessam operations in homology, which are similar to Massey operations in cohomology but are independent of them. Additionally, it defines and analyzes $A_n$-maps, which are special types of maps between associative H-spaces, and their relationship to the Dold and Lashof construction. The paper applies these concepts to Postnikov systems of $A_n$-spaces, particularly those with just two nontrivial homotopy groups. Finally, it examines the obstruction theory for $A_n$-maps and the classification of loop classes.