A comprehensive numerical study of the spin toque driven dynamic states is presented for a synthetic ferrimagnet. For this, the Landau-Lifshitz-Gilbert equation has been solved simultaneously for the two coupled layers of the synthetic ferrimagnet in a macrospin approach including the spin transfer torque term from an external polarizer for one of them. It is shown that a large variety of dynamic modes (in-plane precession (IPP) and out-of-plane precession) can be established, upon varying the strength of the exchange bias field that pins one of the layers of the SyF as well as the Ruderman-Kittel-Kasuya-Yosida interlayer coupling strength. The current—field state diagrams are presented as well as the frequency current dependencies of the most important mode which is the IPP mode. A characteristic feature of the IPP mode for the coupled system (as compared to single layer excitations) is the change, increase or decrease of the frequency, with current upon increasing field. It is shown that this strongly depends on the asymmetry of the internal fields that the two layers experience, upon varying either their thickness or the exchange bias field.