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Previous studies of the electronic spectrum of $BO2$ observed in $absorption,1,2$ $emission3$ and by argon ion laser-excited $fluorescence4$ have revealed that the characterization of the energy levels of this molecule is complicated by the combined effects of spin-orbit coupling, the Renner effect and Fermi resonance. In unraveling these effects it becomes essential to have firmly established vibrational assignments for transitions involving all levels of the various Fermi polyads, for example, the (100,020), (110,030) and (200,120,040) polyads. Rotational analysis may provide the necessary confirmation of vibrational assignments, but it requires considerable effort, and it is not possible in some cases because of low intensity or overlapping structure. In view of these difficulties in the $BO2$ analysis, we have examined the resonance fluorescence spectra resulting from selective excitation of the levels in the excited state polyads indicated above. Most of these levels were populated by excitation from the 000 $X2\Pi g$ level of $\mathrm{<mrow\; data-mjx-texclass="ORD">11</mrow>}BO2$ with a nitrogen-pumped dye laser operating between 4891 and 5470 {\AA} with a bandwidth of about 0.4 {\AA}. Our observations provide additional confirmation for most of the vibrational assignments given by $Johns,1$ and they have resulted in the assignment of more than fifty new transitions involving the 100, 020, 200, 120, 040 levels in both the $A2\Pi$ and $X2\Pi$ states of $\mathrm{<mrow\; data-mjx-texclass="ORD">11</mrow>}BO2$. In addition, about five transitions of $\mathrm{<mrow\; data-mjx-texclass="ORD">10</mrow>}BO2$ were observed which confirm the 020 $(P=3/2,\ell =0,2)$ and 100 (P = 3/2) ground state vibronic levels assigned by $Dymek.2$