Аннотация:We report nuclear quadrupole resonance (NQR) and nuclear magnetic resonance (NMR) measurements of the spin lattice and Gaussian spin-spin relaxation times, ${T}_{1}$ and ${T}_{2G}$, respectively, in an unaligned (NQR) and aligned (NMR) powder of Y${\mathrm{Ba}}_{2}$${\mathrm{Cu}}_{4}$${\mathrm{O}}_{8}$. Experimental details, critical for accurate NQR measurements in this system, are discussed. The normal-state data are analyzed using several models. Evidence for the existence of a spin gap is presented. The normal-state data agree well with an analysis using scaling theory predictions for $z=1$ quantum critical and quantum disordered regimes. The superconducting state data agree with recent calculations for $d$-wave superconductivity.