There are now at least five sources classified as Soft X-ray Transient
s (SXTs) which show light curve modulations during their active states
that are reminiscent of superhumps in SU UMa stars. We compare the mo
rphology of the humps in SXTs with those in SU UMa stars and find that
they are more analogous to the small subclass of ER UMa systems than
to the bulk of the SU UMa's. The ER UMa stars apparently differ from o
ther SU UMa systems only in having a much higher mass-transfer rate, o
ne that is close to the stability limit of the thermal instability in
the disc. In general SU UMa stars have very low-mass Roche-lobe fillin
g components because a low mass ratio is required to excite the resona
nt instability, that probably drives the superhumps, in the outer edge
of their accretion discs. If the degenerate components of SXTs are bl
ack holes rather than white dwarfs the system and hence the Roche-lobe
filling component can be much more massive and still excite superhump
s. Because X-ray irradiation of the disc by a central accreting neutro
n star or black hole stabilizes the thermal instability at lower mass-
transfer rates, it is difficult to get transient behaviour in black-ho
le systems. Thus, mass-transfer rates in SXTs must naturally be close
to the instability limit, and consequently these systems are similar t
o ER UMa stars in this sense. We test the determination of the mass, o
r at least a lower limit on it, of the compact primary of SXTs by mean
s of the superhump period. (C) 1997 Elsevier Science B.V.