We study, for the first time, the relations of two strong diffuse bands (DIBs) at 9633 and 9577~AA, commonly attributed to C$_{60}^+$, to other interstellar features seen in optical and UV spectra including H{sc i}, Ca{sc i}, Fe{sc ii}, Na{sc i}, Ti{sc ii}, CN, CH, CH$^+$, and C$_2$ and DIBs 5780, 5797, 6196, 6269, 6284, and 6614. We analyzed 62 lines of sight where the stellar contamination by Mg{sc ii} was corrected or found negligible for DIB 9633. Equivalent widths of DIB 9577 were measured in 62 lines of sight. Poor mutual correlation between the strengths of the above features and the major diffuse bands (5780 and 5797) as well as with other DIBs (with some exceptions) were revealed. The considered DIBs are also poorly correlated with the features of neutral hydrogen, molecular carbon, and those of simple interstellar radicals. Perhaps this phenomenon can be explained if the diffuse band 9577 is an unresolved blend of two or more interstellar features. There are indications that 9633 and 9577 diffuse bands are stronger in $sigma$-type clouds, i.e. these features resemble the behavior of reasonably broad DIBs, which are strong in the lines of sight where the UV flux from the very hot nearby stars plays an important role.
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