The period (in the order of 40 to 80 days) in periodic chronic myelogenous leukemia (PCML) oscillations is quite long compared with the duration of the cell cycle of the hematopoietic stem cells from which the oscillations are presumed to originate (in the order of one or two days). Our objective is to understand the origin of these long-period oscillations using a G0 model for stem cell dynamics. We determine the local stability conditions and show under what conditions the Hopf bifurcation may occur. We interpret the role of each parameter in the loss of stability, and then examine a simpler model to try to deduce possible changes at the stem-cell level that might be responsible for the characteristics PCML.