  We describe the effects of both magnetic buoyancy and differential rotation
on a disc of isothermal gas embedded in a purely azimuthal magnetic field, in
order to study the evolution and interplay of Parker and shearing
instabilities. Both instabilities occur on the slow MHD branch of the
dispersion relation, and can affect the same waves. We put a stress on the
natural polarization properties of the slow MHD waves to get a better
understanding of the physics involved. The mechanism of the shearing
instability is described in details. Waves with a vertical wavelength shorter
than the scale height of the disc are subject to both the Parker and the
transient shearing instabilities. They occur in different ranges of radial
wavenumbers, \ie at different times in the shearing evolution ; these ranges
can overlap or, on the contrary, be separated by a phase of wave-like
oscillations, depending on the strength of differential rotation. Our results
can be applied to both galactic and accretion discs.
