For　unipolar　hydrodynamic　model　of　semiconductor　device　represented　by　Euler-Poisson　equations,　when　the　doping　profile　is　supersonic,　and　the　boundary　data　are　in　subsonic　region　and　supersonic　region　separately,　the　system　possesses　the　shock　transonic　steady-states　and　the　smooth　transonic　steady-states.　In　this　paper　we　study　the　nonlinear　structural　stability　and　the　linear　dynamic　instability　of　these　steady　transonic　solutions.　For　any　relaxation　time:　0　＜　t　＜=　+infinity　,　by　means　of　elaborate　singularity　analysis,　we　first　investigate　the　structural　stability　of　the　C-1-smooth　transonic　steady-states,　once　the　perturbations　of　the　initial　data　and　the　doping　profiles　are　small　enough.　We　note　that,　when　the　C-1-smooth　transonic　steady-states　pass　through　the　sonic　line,　they　produce　singularities　for　the　system,　and　cause　some　essential　difficulty　in　the　proof　of　structural　stability.　Moreover,　when　the　relaxation　time　is　large　enough　t　＞＞　1,　under　the　condition　that　the　electric　field　is　positive　at　the　shock　location,　we　prove　that　the　transonic　shock　steady-states　are　structurally　stable　with　respect　to　small　perturbations　of　the　supersonic　doping　profile.　Furthermore,　we　show　the　linearly　dynamic　instability　for　these　transonic　shock　steady-states　provided　that　the　electric　field　is　suitable　negative.　The　proofs　for　the　structural　stability　results　are　based　on　singularity　analysis,　a　monotonicity　argument　on　the　shock　position　and　the　downstream　density,　and　the　stability　analysis　of　supersonic　and　subsonic　solutions.　The　linear　dynamic　instability　of　the　steady　transonic　shock　for　Euler-　Poisson　equations　can　be　transformed　to　the　ill-posedness　of　a　free　boundary　problem　for　the　Klein-Gordon　equation.　By　using　a　nontrivial　transformation　and　the　shooting　method,　we　prove　that　the　linearized　problem　has　a　transonic　shock　solution　with　exponential　growths.　These　results　enrich　and　develop　the　existing　studies.　(c)　2022　Elsevier　Inc.　All　rights　reserved.