Abstract. A characterization of subdirectly irreducible bands equipped with an involution is given and their properties are investigated. Also, subdirectly irreducibles in the varieties of semilattices with involution and some other interesting classes are discussed in more detail.

AMS Subject Classification (1991): 20M10, 08B26

Received September 5, 2000, and in revised form February 12, 2001. (Registered under 2803/2009.)