The question of the possibility of competing radiations exhibiting different angular distributions (in the sense that one radiation is isotropic and another anisotropic) is investigated. Except for the singular cases $\frac{3}{2}\to \frac{3}{2}$ and 5→4 by quadrupole emission, our conclusion is as follows: if one radiation of multipole order $2^L$ is observed to be isotropic, all competing gamma-radiation will be isotropic if $L\ge j-\frac{1}{2}$, where $j$ is the angular momentum of the emitting state. The possibility of occurrence of singular cases, for which the conclusion would not apply, has been investigated for all radiations for which $L\le 3$. In the case $\frac{3}{2}\to \frac{3}{2}$, $L=2\mathrm{}$ the radiation is isotropic and the applicability of this to the problem of the excited state of ${\mathrm{Li}}^7$ is briefly discussed.

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