We　study　the　ground　states　of　the　single-　and　two-qubit　asymmetric　Rabi　models,　in　which　the　qubit–oscillator　coupling　strengths　for　the　counterrotating-wave　and　corotating-wave　interactions　are　unequal.　We　take　the　transformation　method　to　obtain　the　approximately　analytical　ground　states　for　both　models　and　numerically　verify　its　validity　for　a　wide　range　of　parameters　under　the　near-resonance　condition.　We　find　that　the　ground-state　energy　in　either　the　single-　or　two-qubit　asymmetric　Rabi　model　has　an　approximately　quadratic　dependence　on　the　coupling　strengths　stemming　from　different　contributions　of　the　counterrotating-wave　and　corotating-wave　interactions.　For　both　models,　we　show　that　the　ground-state　energy　is　mainly　contributed　by　the　counterrotating-wave　interaction.　Interestingly,　for　the　two-qubit　asymmetric　Rabi　model,　we　find　that,　with　the　increase　in　the　coupling　strength　in　the　counterrotating-wave　or　corotating-wave　interaction,　the　two-qubit　entanglement　first　reaches　its　maximum　and　then　drops　to　zero.　Furthermore,　the　maximum　of　the　two-qubit　entanglement　in　the　two-qubit　asymmetric　Rabi　model　can　be　much　larger　than　that　in　the　two-qubit　symmetric　Rabi　model.　©　2014,　Springer-Verlag　Berlin　Heidelberg.