Fast (10-30 microm/s) calcium waves can be propagated through all nucleated eukaryotic cells that have been tested as well as certain cell-free extracts. In a widely used model, they are propagated by a reaction-diffusion cycle in which calcium ions diffuse along the outside of endoplasmic reticula and induce their own release from calsequestrin or calreticulin molecules stored within the reticulum's lumen. Here we propose a new tandem wave model in which they are also propagated by a reaction-diffusion cycle within a reticulum's lumen. In this cycle, increases in luminal [H(+)] induce proton release from luminal calsequestrin or calreticulin. The released protons diffuse ahead to where they release more protons from these luminal storage proteins. What might be called proton induced proton release. They also raise luminal electropositivity. The resultant luminal waves are coordinated with extrareticular ones by movements of calcium and hydrogen ions through the reticular membrane. This model makes five testable predictions which include the autorelease of protons in solutions of calsequestrins or calreticulins as well as waves of increased [H(+)], of increased [Ca(2+)] and of more positive voltage within the reticula of whole cells. Moreover, under some conditions, such luminal waves should cross regions without cytosolic ones.