  This paper is devoted to phenomenological study of $\chi_{c,b}$-mesons
production in high energy hadronic collisions in the framework of NRQCD. We
analyze all available experimental data on $\chi_c$-mesons production and
extract non-perturbative NRQCD matrix elements from fitting the data. We show,
that measured $p_T$-spectrum of $\chi_c$-mesons is mainly formed by color
singlet components, while $\sigma(\chi_{c2})/\sigma(\chi_{c1})$ ratio depends
strongly on color octet matrix elements; this ratio becomes a highly sensitive
tool to study contribution of different terms from the NRQCD expansion.
Obtained using NRQCD scaling rules predictions for $\chi_b$-mesons cross
sections are also given.
