The HVDC technology has driven the attention of power systems protection researchers to its impacts over protective schemes of AC transmission lines (TL) connected in the near vicinity of line-commutated converters (LCC). In the literature, it is reported that phasor estimation processes used in traditional protection schemes can lead its functions to misoperate when the commutation failure (CF) phenomena occur. In contrast, reports on the operation of time-domain protection schemes under the mentioned conditions are scarce. In this context, the study could have been carried out via an actual relay, but this does not provide the performance of the internal variables in order to allow a complete understanding of its operation. Therefore, in this paper, a time-domain-based relay model developed in the Alternative Transients Program (ATP) environment, is presented and applied in an AC TL, connected next to an LCC-HVDC link, to assess the performance of two time-domain protective schemes, TD32 and TD21, under CF scenarios allowing analysis of its internal operating quantities. As result, it is shown that despite the distortions caused by the CF in the voltage and current waveforms, the time-domain functions work reliably and fast, but some recommendations should be considered.