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The magneto-rotational decay instability (MRDI) of thin Keplerian discsthreaded by poloidal magnetic fields is introduced and studied. The linearmagnetohydrodynamic problem decouples into eigenvalue problems for in-planeslow- and fast- Alfv'een-Coriolis (AC), and vertical magnetosonic (MS)eigenmodes. The magnetorotational instability (MRI) is composed of a discretenumber of unstable slow AC eigenmodes that is determined for each radius by thelocal beta. In the vicinity of the first beta threshold a parent MRI eigenmodetogether with a stable AC eigenmode (either slow or fast) and a stable MSeigenmode form a resonant triad. The three-wave MRDI relies on the nonlinearsaturation of the parent MRI mode and the exponential growth of two daughterlinearly stable waves, slow-AC and MS modes with an effective growth rate thatis comparable to that of the parent MRI. If, however, the role of the ACdaughter wave is played by a stable fast mode, all three modes remain bounded.

Resonant instability of the nonlinearly-saturated magnetorotational mode in thin Keplerian discs