  Superconductivity (SC) may microscopically coexist with density wave (DW)
when the nesting of the Fermi surface (FS) is not perfect. There are, at least,
two possible microscopic structures of a DW state with quasi-particle states
remaining on the Fermi level and leading to the Cooper instability: (i) the
soliton-wall phase and (ii) the small ungapped Fermi-surface pockets. The
dispersion of such quasi-particle states strongly differs from that without DW,
and so do the properties of SC on the DW background. The upper critical field
$H_{c2}$ in such a SC state strongly increases as the system approaches the
critical pressure, where superconductivity first appears. $H_{c2}$ may
considerably exceed its typical value without DW and has unusual upward
curvature as function of temperature. The results obtained explain the
experimental observations in layered organic superconductors
(TMTSF)$_{2}$PF$_{6}$ and $\alpha $-(BEDT TTF)$_{2}$KHg(SCN)$_{4}$.
