Abstract. Let $\langle\underline k,\leq\rangle $ denote the chain on $k$ elements, $k \geq2$. We present an effective procedure to determine, given a set $F$ of isotone operations on $\langle\underline k,\leq\rangle $, if it generates the whole clone of isotone operations or not. We determine all maximal subclones of ${\rm Pol}\leq $ specified by relations of arity $2$, $(k-1)$ or $k$, and give several examples of maximal subclones. For $k \leq5$ we characterize the maximal subclones of ${\rm Pol}\leq $, and exhibit minimal generating sets.

AMS Subject Classification (1991): 08A40, 06A06

Received August 16, 1993 and in revised form March 16, 1994. (Registered under 5590/2009.)