The transient behaviour of a packed column is considered. The column, uniformly packed on a macroscopic scale, is multi-structured on the microscopic level: the solid phase consists of particles, which may differ in incidence, shape or size, and other relevant physical properties. Transport in the fluid phase happens by convective flow and longitudinal diffusion. The adsorption rate in the column is determined by the combined effects of mass transfer through a thin liquid film around the particles, diffusion into the particles and first-order loss in the particles. An analytical solution to the problem is given in the form of an infinite integral. The solution method is worked out in detail for three special cases, each with only one type of particle in the solid phase, in the shape of a sphere, or a finite cylinder, or a rectangular parallelepiped.