A study is presented of the absorption of an electromagnetic wave in a plasma with a diffuse boundary in a magnetic field of arbitrary direction for the case where the particle concentration decreases exponentially. A system of functional equations has been derived for the Laplace transforms of the electromagnetic field. A study has been made of the relationship between this system and the equations for the Fourier component of the field in a homogeneous plasma. The solutios to the equations in particular cases are discussed, together with the scope for solution in the general case.