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Numerous High‐Voltage Direct Current (HVDC) interconnections in a bipolar configuration are currently in the design phase and set to become operational in the next decade. In the meantime, the shift from Synchronous Generators (SGs) to converter‐interfaced units is raising concerns over the stability of power systems. Grid‐Forming (GFM) control in converters, as opposed to Grid‐Following (GFL) mode, is anticipated to replicate, to some extent, the stabilizing behaviour of SGs. An open research question is whether mimicking the behaviour of SGs with GFM converters would, in turn, induce sub‐synchronous oscillations similar to those present in power systems dominated by SGs. This paper investigates sub‐synchronous interactions between converters and asynchronous AC systems at the terminals of a bipolar HVDC connection. A modal analysis based on a state‐space approach reveals the participation of converters as well as the influence of control modes and system parameters on these low‐frequency oscillations. Time‐domain simulations of a non‐linear model in EMTP software support the findings of the modal analysis. [ABSTRACT FROM AUTHOR]