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The both total and binding energies of the (1,1)-states in the weakly-boundthree-body muonic $d d \mu$ and $d t \mu$ ions are determined to high numericalaccuracy. The binding energy of the (1,1)-state in the muonic $d t \mu$ ion isevaluated as $\varepsilon(d t \mu)$ = -0.66033003831(30) $eV$, while for thesame state in the muonic $d d \mu$ ion we have found that $\varepsilon(d d\mu)$ = -1.9749806166970(30) $eV$. These energies are the most accuratenumerical values obtained for these systems and they are sufficient for allcurrent and future experimental needs.

On the weakly-bound (1,1)-states in the three-body $d d \mu$ and $d t \mu$ muonic ions