Context :

Aims : 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 .

Methods : We subtract the donor star contribution from the composite spectra of DQ Vel using a synthetic spectrum as a donor template .
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 use Gaussian fits to measure the equivalent widths ( EWs ) of Balmer and helium lines in the separated spectra during the long-term cycle and thus analyse EW variabilities .
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 .

Results : 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 where DQ Vel has lost mass at some stage of its binary history , 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 \times 10 ^ { 7 } \mathrm { yr } and is currently in a low mass transfer rate ( -9.8 \times 10 ^ { -9 } \mathrm { M _ { \odot } / 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 .

Conclusions :