The effect of weak static (DC) and alternating (AC) magnetic fields (MFs), as well as combined (AC/DC) collinear MFs on the intensity of morphogenesis processes in the planarian Dugesia (Girardia) tigrina has been studied. It was found that combined MFs produce a stimulating effect on the fission and regeneration of planarians. Both components of the combined MFs, the direct (DC) and the alternating (AC), are important in the realization of the effects of weak MFs. The practically complete absence of one of the components (DC) reverses the sign of the effect. It was shown that the presence of concomitant background MFs does not substantially influence the effects of combined MFs with a very small AC component (100 nT). The effect of the "zero" field is significant and comparable in magnitude with the effects of combined MFs at effective frequencies. Narrow zones of effective amplitudes (in the region of tens and hundreds of nT) of the AC component of the combined MFs, with the DC component close to the value of the geomagnetic field were found, which alternate with regions where the response of the biological object to the influence is absent.