The magnetic and structural properties of YMn_{2} are strongly influenced by introduction of hydrogen (deuterium) in the structure, however, it only slightly modifies the noncollinear antiferromagnetic structure of the compound. The temperature dependences of the NMR relaxation times T_{1} and T_{2} of deuterium and the zero-field relaxation of muons in YMn_{2}D_{x} were measured at temperatures above the magnetic ordering temperature T_{N}. The corresponding relaxation rates are described by the empirical expression (T/T_{N}-1)^{-η}, where the exponent η increases linearly with deuterium concentration x. To explain this behaviour, the Moriya theory of spin fluctuations was used. The expressions for NMR and μSR relaxation rates have been calculated. The resultant formulae agree well with the experiment, giving reasonable values of fitting parameters. The results obtained are discussed in terms of spin fluctuation excitation spectrum.