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The viability of two different classes of $\Lambda(t)$CDM cosmologies istested by using the APM 08279+5255, an old quasar at redshift $z = 3.91$. Inthe first class of models, the cosmological term scales as $\Lambda(t)\simR^{-n}$. The particular case $n=0$ describes the standard $\Lambda$CDM modelwhereas $n=2$ 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 Gyrthe 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. Thesecond class of models is the one recently proposed by Wang and Meng whichdescribes several $\Lambda(t)$CDM cosmologies discussed in the literature. Byassuming that the true age is 2 Gyr it is found that the $\epsilon$ parametersatisfies 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 thebaryonic component is included.Comment: 7 pages, 3 figures, job presented at the IWARA 2005. Revised paper to  match version to be published on GR

Constraints from the old quasar APM 08279+5255 on two classes of Λ(t)-cosmologies