The time-dependent light scattering signatures for singly and multiply stranded polymers of arbitrary shape undergoing random and endwise degradation are developed. For the case of random scission, useful generalizations at low scattering angle are found for linear polymers of arbitrary conformation and any initial polydispersity, which permit deductions to be made concerning the degree of association of the polymer (single, double, triple strand, mixtures, etc.), in addition to determination of absolute polydispersity-independent depolymerization rates. For the particular case of random scission of multiply stranded random coils the form factor is shown to be the Debye function whose usual argument is simply translated by a function dependent on the average number of cuts per original strand and on the number of strands and monomers per strand. The contrasting case of end-wise cleavage (e.g., "exocydic" enzymatic cleavage) is also presented.