The present study discussed the effect of rotation and gravitational on a nonlocal two-temperature thermoelastic solid with variable thermal conductivity. The problem is solved using the dualphase-lag model, coupled theory (CD), and Lord-Shulman (L-S) theory with memory-dependent derivatives. Using suitable non-dimensional variables and normal mode analysis is considered to solve the problem. MATLAB software is used for numerical calculations. Comparisons are made with the results of three different theories predicted in the absence and presence of the gravity field and rotation. Comparisons are made with the results of three different theories predicted for different values of a nonlocal parameter. It is found that the physical quantities are affected by the rotation, gravity field, and the nonlocal parameter.