Angular correlations between $K$ and $L$ x rays in Ta and Tl were measured. The $K$ x rays were detected with a NaI(Tl) crystal, and the $L$ x rays with a Ge(Li) spectrometer. The angular-correlation functions for the $K-L\alpha$ and $K-L\beta$ cascades in Ta were found to be $W\left(\theta \right)=1+(2.48\mathrm{}\pm 0.41)\times {10}^{-2\mathrm{}}{P}_2\left(cos\theta \right)$ and $W\left(\theta \right)=1-(0.12\mathrm{}\pm 0.46)\times {10}^{-2\mathrm{}}{P}_2\left(cos\theta \right)$, respectively. The result for the $K-L\alpha$ cascade is in fair agreement with theory, while the result for the $K-L\beta$ cascade deviates significantly from the theoretical prediction. The angular-correlation functions for the $K-L\alpha$, $K-L\beta$, and $K-\mathrm{Ll}$ cascades in Tl were found to be $W\left(\theta \right)=1+(3.63\mathrm{}\pm 0.32)\times {10}^{-2\mathrm{}}{P}_2\left(cos\theta \right)$, $W\left(\theta \right)=1+(1.31\mathrm{}\pm 0.36)\times {10}^{-2\mathrm{}}{P}_2\left(cos\theta \right)$, and $W\left(\theta \right)=1+(21.8\mathrm{}\pm 2.0)\times {10}^{-2\mathrm{}}{P}_2\left(cos\theta \right)$. These results are in relatively good agreement with theory when the $M2\mathrm{}$ admixtures in the x-ray transitions are taken into account. Better agreement with theory would be obtained for slightly higher $M2\mathrm{}$ admixtures in the $L$ x-ray transitions than theoretically calculated on the basis of an independent-particle model.

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