The AC magnetic susceptibilities in weak magnetic fields, with and without the presence of an applied DC magnetic field, have been performed to study the basic magnetic properties of the layered colossal magnetoresistance (CMR) compounds La1+xSr2-xMn2O7 with x = 0-0.4. A great number of peaks are evident in the temperature dependence of the AC susceptibility, and the peaks become better defined as the La concentration x is increased. The observed peaks may be grouped into four types according to their behavior under an applied DC held. Among them, the peaks associated with the quasi-2D bilayered Mn ordering, CMR effect, and 3D Mn ordering are recognized. The fourth one may possibly be due to charge ordering. (C) 1999 Elsevier Science B.V. All rights reserved.