We study the spectral properties of two kinds of derivatives of the carbon fullerene C(60), small fullerenes and Si-heterofullerenes, by ab initio calculations. The principal method of study is the time-dependent density-functional theory in its full time-propagation form. C(20), C(28), C(32), C(36), and C(50), the most stable small fullerenes in the range of C(20)-C(50), are found to have characteristic features in their optical absorption spectra, originating from the geometry of the molecules in question. The comparison of measured and calculated absorption spectra is found to be a useful tool in differentiating between different, almost isoenergetic ground state structure candidates of small fullerenes. Substitutionally doped fullerenes are of interest due to their enhanced chemical reactivity. It is suggested that the doping degree can be obtained by studying the absorption spectra. For example, it is observed that the spectra gradually change when doping C(60) up to C(48)Si(12) so that absorption in the visible and near infrared regions increases.