We present the first calculations and computer simulations of the static structure and ionic transport properties of molten thallium halides near melting. The calculations have been carried out using the hypernetted-chain theory of liquids (HNC), and for the simulations we have used molecular dynamics (MD). The potentials used for the calculations have the same functional form as the semiempirical potential originally proposed by Vashishta and Rahman (Vashishta P and Rahman A 1978 Phys. Rev. Lett. 40 1337) for studying alpha-AgI.