Verified answer

I'm sorry that I'm not going to be able to give you a clean, straight answer to this. Archaebacteria reproduce in the ways that bacteria can reproduce. They for sure reproduce asexually (through binary fission) but they also have sexual-like modes of reproduction. They are not officially sexual reproduction, but they are like sexual reproduction in that genetic material is exchanged. These modes of reproduction are transformation, transduction, and conjugation. Conjugation is as close to sexual reproduction as it can get. So I can tell you that they are asexual, but they are not technically sexual (there is an exchange of genetic material, but not in a sexual manner). I guess your answer will kind of depend on the way your teacher (or your book) defines sexual reproduction. I would maybe see what your book says about bacteria, because their reproduction modes are very similar.

Archaebacteria reproduce by an asexual process known as binary fission. ... sexual reproduction is not seen in archaebacteria. ...