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In the first half of this paper, dynamic characteristics of conventional decoupler equipped hydraulic mounts are discussed and the demerits of this type of mounts are clarified particularly in case of superimposed inputs and inputs in a high frequency range, say, 300 Hz or more. It is mentioned that decouplers with weak non-linear structures are more effective against superimposed inputs. Concerning inputs in a high frequency range, our newly developed hydraulic mounts which can achieve low dynamic stiffness up to 800 Hz by utilizing liquid-column-resonance against rubber surging of main elastic bodies are explained in details. In the latter half of this paper, the possibility of semi-actively controlled mounts incorporating electro-rheological (ER) fluids into hydraulic mounts are discussed from the theoretical point of view based upon the experimental results taking a simple one-degree-of-freedom vibrational system for example.