  Quasiperiodic eruptions (QPEs) from low-mass galaxy centres may result from
accretion from a white dwarf in a very eccentric orbit about the central
massive black hole. Evolution under gravitational radiation losses reduces the
separation and eccentricity. I note that below a critical eccentricity $e_{\rm
crit} \simeq 0.97$, the accretion disc's viscous timescale at pericentre
passage is probably longer than the orbital period $P$, and periodic eruptive
behaviour is no longer possible. These QPE descendant systems (QPEDs) are then
likely to produce quasiperiodic oscillations (QPOs) rather than eruptions,
varying more smoothly over the orbital cycle, with duty cycles $\sim1$. I
identify 2XMM J123103.2+110648 ($P \simeq 3.9$~hr) and (more tentatively) RE
J1034+396 ($P \simeq 1$~hr) as candidate systems of this type, and find
agreement with their deduced eccentricities $e < e_{\rm crit}$. The absence of
eruptions and the lower accretion luminosities resulting from the smaller
gravitational radiation losses may make QPED systems harder to discover.
Ultimately they must evolve to have viscous times much longer than the orbital
period, and either remain steady, or possibly have infrequent but large
outbursts. The latter systems would be massive analogues of the soft X-ray
transients produced by low stellar-mass X-ray binaries.
