Dispersion properties of slow electromagnetic surface waves propagating on the harmonics of the electron cyclotron frequency across the external steady magnetic field are studied in the case when the magnetic field is parallel to the plasma - metal interface. Theoretical investigation of these surface modes is carried out using the kinetic description under the condition of weak plasma spatial dispersion, when the radii of the charged plasma particles' Larmor rotation are much less than the spatial scale of the considered wave perturbation. The effect of the plasma density transverse inhomogeneity, of plasma particles' concentration and of the external magnetic field value on the dispersion properties of the surface waves on electron cyclotron harmonics (SWCH) is researched.