  We introduce the notion of a ribbon-clasp surface-link, which is a
generalization of a ribbon surface-link. We generalize the notion of a normal
form on embedded surface-links to the case of immersed surface-links and prove
that any (immersed) surface-link can be described in a normal form. It is known
that an embedded surface-link is a ribbon surface-link if and only if it can be
described in a symmetric normal form. We prove that an (immersed) surface-link
is a ribbon-clasp surface-link if and only if it can be described in a
symmetric normal form. We also introduce the notion of a ribbon-clasp normal
form, which is a simpler version of a symmetric normal form.
