Cooperative effects in the fluorescence of two dipole-interacting atoms, wi
th macroscopic quantum jumps (light and dark periods), are investigated. Th
e transition rates between different intensity periods are calculated in cl
osed form and are used to determine the rates of double jumps between perio
ds of double intensity and dark periods, the mean duration of the three int
ensity periods and the mean rate of their occurrence. We predict, to our kn
owledge for the first time, cooperative effects for double jumps, for atomi
c distances from one and to ten wave lengths of the strong transition, The
double jump rate, as a function of the atomic distance, can show oscillatio
ns of up to 30% at distances of about a wave length, and oscillations are s
till noticeable at a distance of ten wave lengths. The cooperative effects
of the quantities and their characteristic behavior turn out to be strongly
dependent on the laser detuning.