The highly excited 4f₇2/¹³6s₁2/(J')np_j(J) Tm states lying near the first two ionisation limits of the atom were investigated. The automatic laser setup used contained three dye lasers pumped by a nitrogen one. The states' energies were measured with an accuracy of +or-0.1 cm^-1. Two excitation schemes were realised. In the first one, the states with J'=3 were excited; the states of this type with n>or approximately=28 are autoionisation states. In the second excitation scheme, the bound Rydberg states with J'=4 were excited. Identification of the observed levels was performed using the calculation of the spectrum made using relativistic perturbation theory with zero-order model approximation. Unambiguous classification was obtained for the following three series: 4f₇2/¹³6s₁2/(3)np₃2/(⁹/₂) (n=26-65), 4f₇2/¹³6s₁2/(4)np₃2/(¹¹/₂) (n=29-57) and 4f₇2/¹³6s₁2/(4)np₁2/(⁷/₂) (n=28-36). For n>27, three shorter series were observed too, for which alternative classifications are possible at the present stage. The experimental results are in very good agreement with the theoretical results, particularly for large values of the principal quantum number n. A peculiar grouping of the states belonging to the different series was observed varying with the variation of n. This confirms the non-Coulombic properties of the highly excited spectrum of the atom considered.