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Strain-gradient effects on the asymptotic near-tip stress and velocity fields of a crack propagating steadily and quasi-statically in an elastic-plastic material displaying linear hardening are highlighted. The flow theory version of couple stress plasticity is adopted for the constitutive description of the material. Under mode I crack propagation a substantial increase of the stress singularity is observed and, thus, of the traction level ahead of the crack-tip, whereas an increase in the shear traction ahead of the crack-tip is noticed under mode II loading conditions.