  We analyze the properties of breathers (time periodic spatially localized
solutions) on chains in the presence of algebraically decaying interactions
$1/r^s$. We find that the spatial decay of a breather shows a crossover from
exponential (short distances) to algebraic (large distances) decay. We
calculate the crossover distance as a function of $s$ and the energy of the
breather. Next we show that the results on energy thresholds obtained for short
range interactions remain valid for $s>3$ and that for $s < 3$ (anomalous
dispersion at the band edge) nonzero thresholds occur for cases where the short
range interaction system would yield zero threshold values.
