It is widely believed that multiwavelength afterglows of gamma-ray bursts (GRBs) originate from relativistic blast waves. We here show that in such blast waves, a significant fraction of the energy of shock-accelerated protons would be lost due to pion production by interactions with afterglow photons. This could lead to long-term production of $10^{16}$--$10^{18}$ eV neutrinos and sub-TeV $gamma$-rays that accompany with usual afterglows, provided that the protons are accelerated to $10^{19}$ eV in the blast waves.
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