Inthepresentpaper,two-andthree-dimensionalvelocitypotentialsgeneratedbypulsatingpressuredistributionsofinfiniteextentonthefreesurfaceofinfinite-depthwatersarestrictlyderivedbasedonspecialcasesofconcentratedpulsatingpressure.Thefar-fieldasymptoticbehaviourofthepotentialsandtheradiationconditionstobesatisfiedbythemarediscussed.Itisprovedinageneralsensethatthepotentialsshouldbecomposedofaforcedwavecomponent,afreewavecomponentandalocaldisturbancecomponent.Theradiationconditionoftheforcedwavecomponentshouldcorrespondtothefar-fieldasymptoticbehaviourofthepressuredistribution,Hence,theformulationofradiationconditionsforthesecond-orderdiffractionpotentialshastheoreticallybecomeclear,Theradiationconditionsfortwo-andthree-dimensionalproblemsareexplicitlygiveninthepaper.