We evaluate the complete leading-order evolution kernels for the chiral-odd twist-3 distributions e( x) and 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.