The paper presents experimental and theoretical studies of two-photon excitation dynamics in 2-methyl-5-tert-butyl-p-quaterphenyl (DMQ) dissolved in cyclohexane/paraffin Experimentally, a two-color two-photon (2C2P) excitation by two femtosecond laser pulses at 800 and 400 nm has been used in combination with the time-resolved detection of polarized molecular fluorescence. The fluorescence decay was found to be two-exponential, resulting in the molecular excited state lifetime of 753 +/- 10 ps and the rotational correlation time of 724 +/- 45 ps. Control over the excited and fluorescent photons polarization has been used for determination from experiment of seven independent molecular parameters. The experimental data were analyzed on the basis of the recent theoretical approach [Shternin, P. S.; Gericke, K-H.; Vasyutinskii, O. S. Mol. Phys. 2010, 108, 813-825) supported by ab initio computations of the DMQ electronic structure and transition dipole moments. The results obtained imply that the photon absorption tensor S is mostly diagonal and that the S-zz component onto the molecular long axis gives the major contribution of 93%. However, it was also found that a number of different symmetry two-photon transitions related to the dipole moment components d(x)d(z) and d(y)d(z) are excited in the conditions of our measurements.