The problem of calculating the ordering and properties of low-lying levels in configurations of the type $5{f}^{n}6d$ falls into four parts: (a) the choice of a coupling scheme to define the basic eigenfunctions; (b) the evaluation of the matrix elements of the spin-orbit interaction and of the Coulomb interaction in the form of linear combinations of certain radial integrals; (c) the estimation of the radial integrals; (d) the diagonalization of the energy matrices. With regard to (a), the $\mathrm{Jj}$ coupling scheme is considered to be the most appropriate; this implies that the Coulomb interaction between the core, comprising the equivalent $f$ electrons, and the $d$ electron (to whose levels the respective symbols $J$ and $j$ refer) is weak compared with the interactions within the two systems. Part (b) is carried out by applying the tensor operator and group theoretical methods of Racah. For (c), values of the Slater integrals ${F}_{k}(5f, 6d)$ and ${G}_{k}(5f, 6d)$ are estimated for various atoms by assuming that they maintain the ratios one to another as they do in Thiii, and that their variation along the actinide series parallels the variation of ${G}^{3}(5f, 7s)$. The last parameter is known for Thiii, and analyses of Uii, Puii, and Amii show that it decreases as one advances along the actinide series. This decline is interpreted as being due to the collapse of the $5f$ shell, and the internal nature of the $5f$ electrons allows some general statements to be made about the spin-orbit coupling constants. Additional information on the parameters is provided by an analysis of the properties of the four lowest levels of Cmi. Part (d) is accomplished for the very lowest levels of ${f}^{2}d$, ${f}^{3}d$, ${f}^{4}d$, ${f}^{8}d$, and ${f}^{10}d$ by the simple expedient of neglecting all off-diagonal elements; for Ui ${f}^{3}d$, where extensive spectroscopic information is available, the interaction of the levels deriving from the $\mathrm{Jj}$ coupling of $^{4}I_{\frac{9}{2}}$ to $^{2}D_{\frac{5}{2}}$ with those deriving from the coupling of $^{4}I_{\frac{11}{2}}$ to $^{2}D_{\frac{3}{2}}$ is included. Where experimental data are available, agreement with the theory, both in respect to the positions of the levels and to their Land\'e $g$ values, is good---often surprisingly so in view of the approximations made.