High-spin states in the odd-odd nucleus $^{168}$Ta have been populated in the $^{120}$Sn($^{51}$V,3n) reaction. Two multi-quasiparticle structures have been extended significantly from spin $sim{20hbar}$ to above ${40hbar}$. As a result, the first rotational alignment has been fully delineated and a second band crossing has been observed for the first time in this nucleus. Configurations for these strongly-coupled rotational bands are proposed based on signature splitting, $B(M1)/B(E2)$ ratio information, and observed rotation-alignment behavior. Properties of the observed bands in $^{168}$Ta are compared to related structures in the neighboring odd-$Z$, odd-$N$, and odd-odd nuclei and are discussed within the framework of the cranked shell model.
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