Self-pulsation effects of cladding-pumped Erbium-Ytterbium co-doped fiber laser (EYDFL) at around the lasing threshold are investigated. It is demonstrated that laser output of the Erbium-Ytterbium co-doped fiber under the bi-directional pumping regime is more stable than that under the unidirectional pumping one due to the relatively uniform pumping of the fiber. Mechanisms of self-pulsations in the laser system are discussed and possible techniques to avoid self-pulsing and stabilize the laser are proposed.