We look at the class
B
n
B_n
which contains those transcendental meromorphic functions
f
f
for which the finite singularities of
f
−
n
f^{-n}
are in a bounded set and prove that, if
f
f
belongs to
B
n
B_n
, then there are no components of the set of normality in which
f
m
n
(
z
)
→
∞
f^{mn}(z)\to \infty
as
m
→
∞
m\to \infty
. We then consider the class
B
^
\widehat B
which contains those functions
f
f
in
B
1
B_1
for which the forward orbits of the singularities of
f
−
1
f^{-1}
stay away from the Julia set and show (a) that there is a bounded set containing the finite singularities of all the functions
f
−
n
f^{-n}
and (b) that, for points in the Julia set of
f
f
, the derivatives
(
f
n
)
′
(f^n)’
have exponential-type growth. This justifies the assertion that
B
^
\widehat B
is a class of hyperbolic functions.