  Search for double $\beta$ decay of $^{136}$Ce and $^{138}$Ce was realized
with 732 g of deeply purified cerium oxide sample measured over 1900 h with the
help of an ultra-low background HPGe $\gamma$ detector with a volume of 465
cm$^3$ at the STELLA facility of the Gran Sasso National Laboratories of the
INFN (Italy). New improved half-life limits on double beta processes in the
cerium isotopes were set at the level of $\lim T_{1/2}\sim 10^{17}-10^{18}$~yr;
many of them are even two orders of magnitude larger than the best previous
results.
