The incoherent quasi-elastic neutron scattering from the heptyl and octyl derivatives of the acta-alkylphthalocyanines, CnPcH2, in their crystalline and liquid crystalline (discotic columnar) phases has been measured. Diffusive motion is observed on the 10-10 to 10-12 s timescale. This is interpreted as alkyl chain motion. A detailed comparison of the mesophase data for C7PcH2 has been made with the predictions of the rotational isomeric state model, and an 2 extra motion on this timescale has been invoked, which probably is a localized translational motion. A small discontinuity in the elastic fraction of the quasi-elastic scattering is consistent with a change in the molecular tilt at the transition between the two Dhd phases.