  A new model for cooling flows in X-ray clusters, capable of naturally
explaining salient features observed, is proposed. The only requirement is that
a significant relativistic component, in the form of cosmic rays (CR), be
present in the intra-cluster medium and significantly frozen to the thermal
gas. Such an addition qualitatively alters the conventional isobaric thermal
instability criterion such that a fluid parcel becomes thermally stable when
its thermal pressure drops below a threshold fraction of its CR pressure.
Consequently, the lowest possible temperature at any radius is about one third
of the ambient temperature {\it at that radius}, exactly as observed, In
addition, we suggest that dissipation of internal gravity waves, excited by
radial oscillatory motions of inward drifting cooling clouds about their radial
equilibrium positions, may be responsible for heating up cooling gas. With the
ultimate energy source for powering the cooling X-ray luminosity and heating up
cooling gas being gravitational due to inward drifting cooling clouds as well
as the general inward flow, heating is spatially distributed and energetically
matched with cooling. One desirable property of this heating mechanism is that
heating energy is strongly centrally concentrated, providing the required
heating for emission-line nebulae.
