  To progress in the comprehension of the double periodic variable (DPV)
phenomenon, we analyse a series of optical spectra of the DPV system DQ Velorum
during much of its long-term cycle. In addition, we investigate the
evolutionary history of DQ Vel using theoretical evolutionary models to obtain
the best representation for the current observed stellar and orbital parameters
of the binary. We investigate the evolution of DQ Vel through theoretical
evolutionary models to estimate the age and the mass transfer rate which are
compared with those of its twin V393 Scorpii. Donor subtracted spectra covering
around 60% of the long-term cycle, allow us to investigate time-modulated
spectral variations of the gainer star plus the disc. We compare the observed
stellar parameters of the system with a grid of theoretical evolutionary tracks
computed under a conservative and a non-conservative evolution regime. We have
found that the EW of Balmer and helium lines in the donor subtracted spectra
are modulated with the long-term cycle. We observe a strenghtening in the EWs
in all analysed spectral features at the minimum of the long-term cycle which
might be related to an extra line emission during the maximum of the long-term
variability. Difference spectra obtained at the secondary eclipse support this
scenario. We have found that a non-conservative evolutionary model is a better
representation for the current observed properties of the system. The best
evolutionary model suggests that DQ Vel has an age of 7.40 x 10^{7} yr and is
currently in a low mass transfer rate (-9.8x10^{-9} Msun/yr) stage, after a
mass transfer burst episode. Comparing the evolutionary stages of DQ Vel and
V393 Sco we observed that the former is an older system with a lower mass
transfer rate. This might explain the differences observed in the physical
parameters of their accretion discs.
