A symmetric tandem mirror plugging a long central cell, with plugs stabilized by a hot‐component plasma is considered. The system is taken to have a flat pressure profile with a steep edge gradient. The interaction of the precessional mode with Alfve´n waves generated in the central cell is then considered. This analysis is noneikonal and is valid whenm&Dgr;/r<1 (mis the azimuthal mode number,rthe plasma radius, and &Dgr; the radial gradient scale length) for long‐wavelength radial modes. Without finite‐Larmor‐radius (FLR) effects the precessional mode is always destabilized by the excitation of the Alfve´n waves form≥2. Form=1, it is possible to achieve stabilization with conducting walls. A discussion is given of how FLR affects stabilization of them≥2 long‐wavelength modes and of FLR stabilization of modes described in the eikonal approximation.