The　problem　of　hypothesis　testing　is　considered　in　the　case　of　observation　of　an　inhomogeneous　Poisson　process　with　an　intensity　function　depending　on　two　parameters.　It　is　supposed　that　the　dependence　on　the　first　of　them　is　sufficiently　regular,　while　the　second　one　is　a　change-point　location.　Under　the　null　hypothesis　the　parameters　take　some　known　values,　while　under　the　alternative　they　are　greater　(with　at　least　one　of　the　inequalities　being　strict).　Four　test　are　studied:　the　general　likelihood　ratio　test　(GLRT),　the　Wald’s　test　and　two　Bayesian　tests　(BT1　and　BT2).　For　each　of　the　tests,　expressions　allowing　to　approximate　its　threshold　and　its　limit　power　function　by　Monte　Carlo　numerical　simulations　are　derived.　Moreover,　for　the　GLRT,　an　analytic　equation　for　the　threshold　and　an　analytic　expression　of　the　limit　power　function　are　obtained.　Finally,　numerical　simulations　are　carried　out　and　the　performance　of　the　tests　is　discussed.　©　2020,　Springer　Nature　B.V.