A weakly nonlinear theory is presented that may explain the persistence of the two main types of low-frequency anomalies observed in the midlatitude jet stream by Dole and Gordon (1983). The theory describes how nonlinearity can balance dispersion effects for both split jet stream anomalies (which resemble blocking flows) and for jet intensification anomalies. It is shown that the variation of the potential or refractive-index function ≡ dq/dψ across the jet stream is crucial for determining which types of anomaly will tend to persist. Although the theory is only weakly nonlinear it is argued that the same dynamical mechanisms will remain important in the high-amplitude regime particularly for the intense-jet anomalies. In the split anomalies the potential vorticity contours can easily become closed at high amplitude hence trapping air parcels (this is the origin of the strongly nonlinear modon solutions). However, even for very strong intense-jet anomalies the potential vorticity contours may remain open and then no air trapping occurs, thus, the variations in the cross jet stream potential function remain important. Initial value numerical experiments are presented to demonstrate that both types of anomaly are close to persistent states of the full barotropic vorticity equation, even at amplitudes that are beyond the strict range of validity of the weakly nonlinear theory. Some discussion and investigation of the possible role of critical lines in preventing dispersion into equatorial latitudes is also presented. Finally, the possibility of testing this theory by making appropriate diagnostic measurements is considered.