New limits on $beta^+$EC and ECEC processes in $^{74}$Se have been obtained using a 600 cm$^3$ HPGe detector and an external source consisting of 1600 g of a natural selenium powder. For different $beta^+$EC and ECEC transitions (to the ground and excited states) obtained limits are on the level $sim (0.2-4.8)times10^{19}$ yr at 90% C.L. In particular, for the potentially resonant transition into the 1204.2 keV excited state of $^{74}$Ge a lower half-life limit of $1.1times10^{19}$ yr at 90% C.L. has been obtained. Possibility to increase the sensitivity of such measurements is discussed.
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