  The viability of two different classes of $\Lambda(t)$CDM cosmologies is
tested by using the APM 08279+5255, an old quasar at redshift $z = 3.91$. In
the first class of models, the cosmological term scales as $\Lambda(t)\sim
R^{-n}$. The particular case $n=0$ describes the standard $\Lambda$CDM model
whereas $n=2$ stands for the Chen and Wu model. For an estimated age of 2 Gyr,
it is found that the power index has a lower limit $n> 0.21$, whereas for 3 Gyr
the limit is $n > 0.6$. Since $n$ can not be so large as $\sim 0.81$, the
$\Lambda$CDM and Chen and Wu models are also ruled out by this analysis. The
second class of models is the one recently proposed by Wang and Meng which
describes several $\Lambda(t)$CDM cosmologies discussed in the literature. By
assuming that the true age is 2 Gyr it is found that the $\epsilon$ parameter
satisfies the lower bound $\epsilon > 0.11$, while for 3 Gyr, a lower limit of
$\epsilon > 0.52$ is obtained. Such limits are slightly modified when the
baryonic component is included.
