A perturbation analysis of the capillary instability of an inviscid liquid jet of circular cross section was carried out to third order. The results show that the nonlinear terms are responsible for the presence of satellite drops. The dimensionless cutoff wavenumber, which separates regions of stability and instability, remains unity to third order. The present theory was used in a computer simulation of jet breakup, and it was found that predicted surface wave profiles, disturbance amplification rates and drop sizes are in excellent agreement with the data of previous investigators. New experimental results are presented as additional support of the theory.