  Using the infrared-renormalon approach, we obtain the constraints on the
next-to-leading order non-singlet polarised parton densities. The advocated
feature follows from the consideration of the effect revealed in the process of
the next-to-leading order fits to the data for the assymetry of polarised
lepton-nucleon scattering which result in the approximate nullification of the
$1/Q^2$-correction to A_1^N(x,Q^2).
