This　paper　presents　a　finite　difference　time　domain　formulation　incorporating　conductor　losses　due　to　skin　and　proximity　effects　for　a　uniform　lossy　two-conductor　transmission　line.　At　high　frequency　the　per-unit-length　effective　internal　impedance　model　is　based　on　a　boundary　element　method　formulation　enforcing　high-order　surface　impedance　boundary　conditions.　A　smooth　transition　from　the　low　to　the　high　frequency　model　is　obtained　using　first-order　low-and　high-pass　filters.　The　effective　internal　impedance　model　is　implemented　into　the　finite　difference　time　domain　method　via　the　discretization　of　the　convolution.　Finally,　a　computationally　efficient　finite　difference　time　domain　discretization　of　the　two-conductor　transmission　line　equation　is　obtained　applying　a　recursive　convolution　technique.　The　proposed　formulation　is　validated　by　comparison　with　the　conventional　inverse　fast　Fourier　transform　method　and　shows　an　improvement　with　respect　to　the　well-known　Paul＇s　method,　which　does　not　consider　the　proximity　effect.　©　2018　IEEE.