The time–latitude distribution of the axisymmetric component of the large scale solar magnetic fields is known to have a pronounced poleward branch at higher latitudes (Stenflo, 1988, 1991, 1994; Stenflo and Gudel, 1988; Ribes and Bonnefond, 1990; Mouradian and Soru-Escaut, 1991). This branch is also present in the butterfly diagram of a number of tracers of the magnetic field such as quiescent filaments, polar faculae, or the coronal green line (Callebaut and Makarov, 1992; Makarov and Sivaraman, 1989; Leroy and Noens, 1983). Several conflicting explanations exist for this polar branch. Noting that the separation latitude of the two branches, 30–40◦, approximately coincides with the latitude where the radial differential rotation changes sign according to helioseismology, one group of theories interprets it as the surface reflection of a high-latitude poleward propagating dynamo wave, coexisting with the low-latitude equatorward wave (Gilman, Morrow, and De Luca, 1989; Belvedere, Pidatella, and Proctor, 1990, 1991). The Parker–Yoshimura rule of sign (Belvedere, 1985) then naturally leads to the correct directions of propagation if α is negative, as expected in the lower overshooting layer where the dynamo should operate. (In fact this is only so for certain latitudinal profiles of α, cf. Schmitt, 1993.) The most modern version of these models, also incorporating some transport effects, is due to Rudiger and Brandenburg (1995). In what follows we will refer to these models as double wave models.