It is proposed to interpret the outbursts of Nova Aquilae 1919 (V605 Aql) and the nova-like outburst of Sakurai’s object in 1996 as recurrent outbursts of classical novae of the DQ Her and RR Pic types with recurrence periods of about 1100 and 50,000 years, respectively, and some characteristics of these stars are derived on that basis. Only now has V605 Aql returned to the quiet state, and it has an absolute visual magnitude no fainter than 8^m−9^m. The orbital inclination of the prenova’s binary system is about 90°. The absolute visual magnitude of the prenova of V4334 Sgr is no brighter than 3^m. It is quite possible that the orbital inclination of the prenova’s binary system is close to 0°. The expansion velocities of the shells are 30–40 km/sec in both cases. The structure of the ejection is conserved in the recurrent outbursts. Translated from Astrofizika, Vol. 42, No. 4, pp. 563–570, October–December, 1999.