Abstract. A clone of operations is called $n$-collapsing if it is uniquely determined by its $n$-ary operations. This paper gives internal and external characterizations of $n$-collapsing clones, for arbitrary positive integers $n$. The strongest results are obtained in the case $n=1$ which is therefore treated separately.

AMS Subject Classification (1991): 08A40, 03B50, 20M20

Received January 30, 1992, and in revised form July 13, 1993. (Registered under 5535/2009.)