The wide application of energy conversion facilities on the demand side (e.g., combined heat and power units) has accelerated the integration of multiple energies in the form of the Energy Hub (EH). EH can schedule its electricity and gas consumption patterns flexibly to provide demand response (DR) services to the electricity system. While DR services from EHs provide support for the electricity system operation, they can also lead to gas demand spikes in return if the DR is not implemented properly. The gas stored in the pipeline (i.e., linepack) is a promising flexible resource to accommodate the gas demand spikes during the DR. However, the linepack is governed by the complex physical characteristics of gas flow dynamics, which are challenging to use. This chapter proposes a coordinated optimal control framework for both EH and integrated electricity and gas systems (IEGS), focusing on utilising the linepack flexibility to promote the DR capability. First, we develop a multi-level self-scheduling framework for the EH to comprehensively explore the DR potential. The constraints of gas flow dynamics are then formulated to ensure that the fluctuating gas demand can be accommodated by the linepack in the IEGS. The second-order cone (SOC) relaxation is adopted to convexify the nonlinearity in the motion equation of gas flow dynamics. Moreover, to tackle the overall mixed-integer SOC programming problem, we propose an enhanced Benders decomposition strategy by embedding the lift-and-project cutting plane method, and further, devise a novel solution procedure. Finally, the IEEE 24-bus Reliability Test System and the Belgium natural gas transmission system are used to validate the effectiveness of the proposed method [40].