  In the last decade, a large amount of research has been concentrated on the
operators living on the model space. Asymmetric truncated Toeplitz operators
and asymmetric truncated Hankel operators are the natural generalization of
truncated Toeplitz operators and truncated Hankel operators respectively. In
this paper, we obtained the basic results concerning the product of these
operators and in terms of product their connection with each other. In
addition, when the inner function has a certain symmetric property, some
algebraic properties of truncated Hankel operators are also discussed.
