This article discusses the evolution of cosmological gamma-ray burst (GRB) remnants, known as GRBR, following a gamma-ray event. The authors predict significant optical emission that should be measurable hours after the event, and radio emission days to weeks after. The flux at optical, X-ray, and other long wavelengths decays as a power of time, with the initial flux and decay exponent helping distinguish between different fireball models. The paper investigates the dynamical evolution of GRBR for both impulsive external shock and wind internal shock models. It shows that both types of cosmological GRBR produce significant amounts of softer radiation, mostly X-rays and optical, but in some cases also radio. The radiation can be detectable with appropriate instrumentation, with the best chances for detection at optical wavelengths. The paper also discusses the spectral evolution of GRBR from impulsive fireballs, showing that the observed flux evolves differently depending on the type of shock physics. For wind fireball models, the GRB spectra are discussed, with the observed fluxes given by equations (1) and (2). The paper concludes that GRBR should leave behind an afterglow at wavelengths longer than gamma-rays, particularly at X-ray, optical, and in some cases radio bands. Observations in other bands can help narrow down the range of models and refine existing ones. The authors suggest that optical detection of GRBR is feasible with modest telescopes, and that repeated observations can help determine the time-decay exponent of the optical flux, which can help discriminate between models. The paper also discusses the potential for radio detection, noting that the synchrotron radio fluxes from GRBR are expected to be very small, but radio searches are worthwhile due to the possibility of coherent emission. The authors thank NASA and the Royal Society for support.This article discusses the evolution of cosmological gamma-ray burst (GRB) remnants, known as GRBR, following a gamma-ray event. The authors predict significant optical emission that should be measurable hours after the event, and radio emission days to weeks after. The flux at optical, X-ray, and other long wavelengths decays as a power of time, with the initial flux and decay exponent helping distinguish between different fireball models. The paper investigates the dynamical evolution of GRBR for both impulsive external shock and wind internal shock models. It shows that both types of cosmological GRBR produce significant amounts of softer radiation, mostly X-rays and optical, but in some cases also radio. The radiation can be detectable with appropriate instrumentation, with the best chances for detection at optical wavelengths. The paper also discusses the spectral evolution of GRBR from impulsive fireballs, showing that the observed flux evolves differently depending on the type of shock physics. For wind fireball models, the GRB spectra are discussed, with the observed fluxes given by equations (1) and (2). The paper concludes that GRBR should leave behind an afterglow at wavelengths longer than gamma-rays, particularly at X-ray, optical, and in some cases radio bands. Observations in other bands can help narrow down the range of models and refine existing ones. The authors suggest that optical detection of GRBR is feasible with modest telescopes, and that repeated observations can help determine the time-decay exponent of the optical flux, which can help discriminate between models. The paper also discusses the potential for radio detection, noting that the synchrotron radio fluxes from GRBR are expected to be very small, but radio searches are worthwhile due to the possibility of coherent emission. The authors thank NASA and the Royal Society for support.