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High-spin structures of holmium ( $Z=67$ ) and erbium ( $Z=68$ ) isotopes are presented near mass 160, a region where collective and single-particle modes of excitation compete in the generation of angular momentum at the highest experimentally attainable spins in atomic nuclei. The level schemes of the ${}^{156,157,158}\mathrm{Ho}$ isotopes have been significantly extended, reaching spins in the $40\hslash$ to $55\hslash$ range, through multiple experiments utilizing the Gammasphere spectrometer. In particular, several new noncollective band-terminating states are reported for these nuclei. The nature of these states, including both valence-space terminations and core-excited oblateconfigurations, is discussed in terms of proton particle-hole (p-h) excitations across the semimagic $Z=64$ shell closure. Cranked-Nilsson–Strutinsky (CNS) calculations have been used to interpret the nature of these noncollective states. The corresponding terminating states in ${}^{154–159}\mathrm{Er}$ are also included, providing a systematic description of band termination in this mass region. In addition, three weak rotational structures have been assigned to ${}^{157}\mathrm{Ho}$ at the highest spins. These collective bands are proposed to be based on a triaxial strongly deformed nuclear shape, involving neutron p-h excitations across the $N=82$ shell gap.