  We investigate the asymptotic number of elements of size $n$ in a particular
class of closed lambda-terms (so-called $BCI(p)$-terms) which are related to
axiom systems of combinatory logic. By deriving a differential equation for the
generating function of the counting sequence we obtain a recurrence relation
which can be solved asymptotically. We derive differential equations for the
generating functions of the counting sequences of other more general classes of
terms as well: the class of $BCK(p)$-terms and that of closed lambda-terms.
Using elementary arguments we obtain upper and lowerestimates for the number of
closed lambda-terms of size $n$. Moreover, a recurrence relation is derived
which allows an efficient computation of the counting sequence. $BCK(p)$-terms
are discussed briefly.
