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The transverse momentum distributions of the strange and double-strange hyperon resonances (Σ(1385)±, Ξ(1530)0) produced in p–Pb collisions at sNN−−−√=5.02 TeV were measured in the rapidity range −0.5<yCMS<0 for event classes corresponding to different charged-particle multiplicity densities, ⟨dNch/dηlab⟩. The mean transverse momentum values are presented as a function of ⟨dNch/dηlab⟩, as well as a function of the particle masses and compared with previous results on hyperon production. The integrated yield ratios of excited to ground-state hyperons are constant as a function of ⟨dNch/dηlab⟩. The equivalent ratios to pions exhibit an increase with ⟨dNch/dηlab⟩, depending on their strangeness content.