This paper discusses some effects of mobile electrons in some antiferromagnetic lattices. It is shown that these electrons (or holes) always give rise to a distortion of the ground state spin arrangement, since electron transfer lowers the energy by a term of first order in the distortion angles. In the most typical cases this results in: (a) a nonzero spontaneous moment in low fields; (b) a lack of saturation in high fields; (c) simultaneous occurrence of "ferromagnetic" and "antiferromagnetic" lines in neutron diffraction patterns; (d) both ferromagnetic and antiferromagnetic branches in the spin wave spectra. Some of these properties have indeed been observed in compounds of mixed valency such as the manganites with low Mn4+ content. Similar considerations apply at finite temperatures, at least for the (most widespread) case where only the bottom of the carrier band is occupied at all temperatures of interest. The free energy is computed by a variational procedure, using simple carrier wave functions and an extension of the molecular field approximation. It is found that the canted arrangements are stable up to a well-defined temperature T1. Above T1 the system is either antiferromagnetic or ferromagnetic, depending upon the relative amount of mobile electrons. This behavior is not qualitatively modified when the carriers which are responsible for double exchange fall into bound states around impurity ions of opposite charge. Such bound states, however, will give rise to local inhomogeneities in the spin distortion, and to diffuse magnetic peaks in the neutron diffraction pattern. The possibility of observing these peaks and of eliminating the spurious spin-wave scattering is discussed in an Appendix.