This work investigates the stability and control of offshore wind farms with high-voltage dc (HVDC) connection to onshore power grids. An impedance-based stability criterion is applied to determine the stability of the offshore ac collection bus and to develop control requirements for the wind inverters as well as the HVDC rectifier built based on voltage-source converters (VSC). Positive- and negative-sequence output impedance of the wind inverters and input impedance of the VSC HVDC rectifier are modeled by the harmonic linearization method. These models are then used to understand the effects of different converters and their control design on the ac bus voltage stability. A resonance is presented as an example to highlight possible instability problems of the offshore ac bus and the ability of the impedance models to predict such instability. Based on the analysis, several control methods to enhance ac bus voltage stability are presented and compared.