  In protoplanetary discs (PPDs) consisting of gas and dust particles, fluid
instabilities induced by the drag force, including secular gravitational
instability (SGI) can facilitate planet formation. Although SGI subject to the
axisymmetric perturbations was originally studied in the absence of gas
feedback and it then generalized using a two-fluid approach, the fate of the
nonaxisymmetric SGI, in either case, is an unexplored problem. We present a
linear perturbation analysis of the nonaxisymmetric SGI in a PPD by
implementing a two-fluid model. We explore the growth of the local,
nonaxisymmetric perturbations using a set of linearized perturbation equations
in a sheared frame. The nonaxisymmetric perturbations display significant
growth during a finite time interval even when the system is stable against the
axisymmetric perturbations. Furthermore, the surface density perturbations do
not show continuous growth but are temporally amplified. We also study cases
where the dust component undergoes amplification whereas the gas component
remains stable. The amplitude amplification, however, strongly depends on the
model parameters. In the minimum mass solar nebula (MMSN), for instance, the
dust fluid amplification at the radial distance 100 au occurs when the Stokes
number is about unity. But the amplification factor reduces as the dust and gas
coupling becomes weaker. Furthermore, perturbations with a larger azimuthal
wavelength exhibit a larger amplification factor.
