Aiming　at　the　problem　that　the　reliability　research　on　hierarchical　hypercube　networks　was　not　yet　systematic,　which　se-verely　restricted　its　application　and　popularization,　the　hierarchical　hypercube　network　was　taken　as　studying　object,　on　the　basis　of　obtaining　the　relevant　topological　properties　of　the　hierarchical　hypercube　network,　the　h-extra　conditional　diagnosability　and　t/s-diagnosability　of　the　n-dimension　hierarchical　hypercube　(HHCn)　network　under　the　PMC　model　and　MM*　model　were　obtained　by　theoretical　deduction.　In　addition,　the　t/s-diagnosis　algorithm　of　HHCn　under　the　PMC　model　and　MM*　model　was　designed　and　its　time　complexity　was　analyzed.　The　re-search　results　show　that　the　h-extra　conditional　diagnosability　of　HHCn　is　about　h+1　times　of　its　traditional　diagnosability,　and　the　t/s-diagnosability　of　HHCn　is　about　s+1　times　of　its　traditional　diagnosability.　Those　results　improve　the　reliability　index　of　the　hierarchical　hypercube　network　and　provide　an　important　theoretical　basis　for　its　application　and　popularization.　©　2021,　Editorial　Board　of　Journal　on　Communications.　All　right　reserved.