According to the current paradigm of circumstellar disk evolution, gas-rich primordial disks evolve into gas-poor debris disks composed of second-generation dust. To explore the transition between these phases, we searched for 12 CO, 13 CO, and C 18 O emission in seven dust-rich debris disks around young A-type stars, using ALMA in Band 6. We discovered molecular gas in three debris disks. In all these disks, the 12 CO line was optically thick, highlighting the importance of less abundant molecules in reliable mass estimates. Supplementing our target list by literature data, we compiled a volume-limited sample of dust-rich debris disks around young A-type stars within 150 pc. We obtained a CO detection rate of 11/16 above a 12 CO J=2-1 line luminosity threshold of ∼1.4×10 4 Jy km s −1 pc 2 in the sample. This high incidence implies that the presence of CO gas in bright debris disks around young A-type stars is likely more the rule than the exception. Interestingly, dust-rich debris disks around young FG-type stars exhibit, with the same detectability threshold as for A-type stars, significantly lower gas incidence. While the transition from protoplanetary to debris phase is associated with a drop of dust content, our results exhibit a large spread in the CO mass in our debris sample, with peak values comparable to those in protoplanetary Herbig Ae disks. In the particularly CO-rich debris systems the gas may have primordial origin, characteristic of a hybrid disk.