In a previous study the Laplace transform has been introduced in order to solve the combined heat and mass transfer problem in absorbing laminar falling films with constant film velocity for an isothermal as well as an adiabatic wall boundary condition. It has been stated, that the Laplace transform basically allows to apply arbitrary wall boundary conditions in contrast to the Fourier method. Therefore, in the present study a diabatic wall boundary condition is applied, which, as limiting cases, includes both the isothermal wall if the thermal resistance of the wall is zero as well as the adiabatic wall condition for an infinite thermal resistance of the wall. Temperature and mass fraction profiles across the film as well as the evolution of the absorbed mass flux with increasing flow length are presented for two different thermal resistances of the wall and modified Stefan numbers. The results are compared to the limiting cases of the isothermal and the adiabatic wall boundary condition. The present study offers an analytical solution with a more realistic boundary condition of a constant thermal resistance of the wall including the isothermal and the adiabatic wall boundary condition. (C) 2014 Elsevier Ltd. All rights reserved.