There is a well-known connection between hyperidentities of an algebra 
and identities satisfied by the clone of the algebra. The clone of 
an algebra is a heterogeneous algebra, and the correspondence between 
hyperidentities and clone identities is rather complicated to work with. 
It is also of interest to study this correspondence in a restricted setting, 
that of hyperidentities of unary algebras (of arbitrary unary type) and 
identities in the unary clone of unary term operations. This unary clone 
is just a monoid, usually called the transition monoid of the unary algebra. 
This correspondence is an important one in automata theory, since 
any finite unary algebra ${\cal A}$ can be regarded as an automaton: 
the set $A$ is regarded as a set of states, with one state chosen 
as an initial state and a subset of $A$ chosen as the set of final states, 
and the operations of the algebra regarded as inputs. 
Then terms and identities over the unary algebra ${\cal A}$ correspond to 
monoid words from the free monoid generated by the operations of ${\cal A}$. 
In this paper we study the correspondence between hyperidentities and 
clone identities in this special case of unary algebras and transition 
monoids. 
We also look at generalizations of this approach to algebras of type $(n,n, \ldots)$, 
and the corresponding $n$-clones, which correspond to tree automata 
of type $(n,n, \ldots)$.