Numerical computations were performed to study light scattering by clusters of up to 200 interacting spheres to better understand the structure of dust particles in the Solar System. The size parameter of a cluster is about 13. We, however, vary several other parameters to see their impact on the scattering of light. The packing density of a cluster varies between 0.1 and 0.2 and the size parameter of a constituent sphere is either 1.2 or 1.9. We use the refractive indices of 1.29 and 1.57 with a small imaginary part. These indices roughly correspond to ice and silicates. The clusters are formed either by the diffusion limited aggregation process or by a random thinning of a maximally packed cluster. All light scattering computations have been done with the discrete-dipole approximation (DDA) which is the most flexible method for complicated cluster geometries. We calculate all the 16 elements of the scattering matrix together with efficiency factors for our model particles in random orientation. The first order scattering approximation, which includes only the electromagnetic phase correction between the constituent particles without any mutual interactions, explains remarkably well the angular dependence (including diffraction) of all the matrix elements below the scattering angle of about 60°. For large scattering angles the signatures of the constituent particles are completely washed out. © 1997 Academic Press.