  We evaluate the complete leading-order evolution kernels for the chiral-odd
twist-3 distributions $e(x)$ and $\widetilde h_L(x)$ of the nucleon. We
establish the connection between the evolution equations in light-cone position
and light-cone fraction representations, which makes a correspondence between
the non-local string operator product expansion and the QCD-inspired parton
model. The compact expression obtained for the local anomalous dimension matrix
coincides with previous calculations. In the multicolour QCD as well as in the
large-$x$ limit the twist-3 distributions obey simple DGLAP equations.
Combining these two limits, we propose improved DGLAP equations and compare
them numerically with the solutions of the exact evolution equations.
