The aim of the present work was to study the cross-section of the (n,2n) and (n,3n) reactions on 203Tl, by irradiating a natural TlCl pellet target with monoenergetic neutron beams at 16.4, and 18.9 MeV. The cross section measurements were carried out using the activation method, with respect to the 197Au(n,2n)196Au and 27Al(n,α)24Na reference reactions. The monoenergetic neutron beams were generated in the 5.5 MV Tandem accelerator of NCSR “Demokritos”, using the 3H(d,n)4He reaction. Monte Carlo simulations have been performed to take into account the gamma-ray self-absorption results as well as the estimation of the neutron flux through the reference foils. Theoretical calculations with the code EMPIRE have also been performed, using the same parameterization implemented in the theoretical study of Ir and Au nuclei in an attempt to find a suitable model for the description of all the experimental results in this mass region.