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A comprehensive study of the effects of hydrogen atom tunnelling on proton magnetic resonance transient responses is reported for B-phase palladium hydride. Data for B-PdH, are presented for concentrations X = 0.80, 0.75 and 0.71 at 40 K and are characteristic of data taken over the temperature range 30 to 80 K. It is shown that the free-induction decay signal can be represented by the same empirical function for each concentration studied. The ratio of second to fourth moments deduced by fitting this function to the data is consistent with a random distribution of hydrogen atoms over the octahedral sites of the Pd lattice. However, the moments themselves are reduced from their rigid lattice values as a result of the tunnelling of the hydrogen atoms. A solid-echo study shows that the direct dipolar coupling between protons is much more important than indirect coupling.The presence of a Hahn echo is related to the distribution of Knight shifts in this nonstoichiometric alloy. The characteristics of this echo are documented.