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The dynamics of phase transitions and their resulting gravitational-wave signal are studied in the conformal (C2HDM) and non-conformal (NC2HDM) CP-conserving 2HDM. Conformal tree-level potentials naturally lead to large supercooling when quantum and thermal corrections are included. We however find that first-order phase transitions are more strongly supercooled in the NC2HDM compared to the C2HDM. Finally, we calculate the gravitational-wave signal for both C2HDM and NC2HDM phase transitions, suggesting their detectability in the latter case by future gravitational-wave detectors such as LISA.