We present the first measurement of two-particle momentum correlations in jets produced in p$\bar{p}$ collisions at center of mass energy of 1.96 TeV. A comparison of the experimental data to theoretical predictions obtained for partons within the framework of resummed perturbative QCD (Next-to-Leading Log Approximation) shows that the predicted parton momentum correlations survive the hadronization stage of jet fragmentation and are present at the hadron level. We also present the measurement of the intrinsic transverse momenta of particles with respect to jet axis (kT). Experimental data is compared to the theoretical predictions obtained for partons within the framework of Modified Leading Log Approximation and Next-to-Modified Leading Log Approximation, and shows good agreement in the range of validity of the theoretical predictions. The results of both measurements indicate that the perturbative stage of the jet formation must be dominant and give further support to the hypothesis of Local Parton-Hadron Duality.