We present the results of 32 nights of CCD photometry of V1974 Cygni, from 1994 and 1995. We verify the presence of two distinct periodicities in the light curve: 0.0812585d~1.95h and 0.0849767d~2.04h. We establish that the shorter periodicity is the orbital period of the underlying binary system. The longer period oscillates with an average value of --/P--~3x10^-7 - typical of permanent superhumps. The two periods obey the linear relation between the orbital and superhump periods that holds among members of the SU Ursae Majoris (SU UMa) class of dwarf novae. A third periodicity of 0.083204 d~2.00h appeared in 1994 but not in 1995; it may be related to the recently discovered anti-superhump phenomenon. These results suggest a linkage between the classical nova V1974 Cyg and the SU UMa stars, and indicate the existence of an accretion disc and permanent superhumps in the system no later than 30 months after the nova outburst. From the precessing disc model of the superhump phenomenon, we estimate that the mass ratio in the binary system is between 2.2 and 3.6. Combined with previous results, this implies a white dwarf mass of 0.75-1.07 Msolar.