A study is made of the stability of the low‐frequency precession and kink modes of a long astron particle layer embedded in a dense low‐temperature plasma. The precessional motion corresponds to a toroidal mode numbern= 1 and the kink motion ton≳ 2. Two types of precession of nonrelativistic ion layers are analyzed in detail. For frequencies &ohgr; such that &agr;2&OHgr;2≪‖&ohgr;‖2≪&OHgr;2, there is a precession mode with the real part of the frequency &ohgr;r≈−(&eegr;e/2) &OHgr;. Here, &OHgr; is the average circulation frequency for the layer ions; &agr;≡ vA/v¯&Vthgr;≪ 1 withvAthe plasma Alfve´n wave speed, and v¯&Vthgr;the average azimuthal velocity of the layer ions; and &eegr;eis the effective external magnetic field index. This mode shows the well known negative energy type of instability due to dissipation for &eegr;e< 0, which corresponds to a mirror field. For frequencies ‖&ohgr;‖2≪&agr;2&OHgr;2, there is a magnetohydrodynamic precession mode with a frequency &ohgr;≈± (&eegr;e/&zgr;)1/2&agr;&OHgr;, where &zgr; is the loading factor, which is a measure of the layer strength. This mode has a magnetohydrodynamic type of instability for &eegr;e< 0. For the kink modes, a necessary and sufficient condition for stability is shown to be &eegr;s< 3, where &eegr;sis the self‐magnetic field index.