de Haas-van Alphen Effect in the High-$T_c$ $A15$ Superconductors ${\mathrm{Nb}}_3$Sn and ${\mathrm{V}}_3$Si

De Haas-van Alphen (dHvA) oscillations have been observed in ${\mathrm{Nb}}_3$Sn in the (110) plane and in ${\mathrm{V}}_3$Si at two orientations using single crystals of high resistance ratio and magnetic fields in excess of $H_{c2\mathrm{}}$. The dHvA frequency data for ${\mathrm{Nb}}_3$Sn can be interpreted as a series of nested ellipsoids centered at $M$, as suggested by a recent high-precision calculation of the ${\mathrm{Nb}}_3$Sn Fermi surface.