In　this　paper,　the　analytical　solutions　for　paired　asymmetric　periodic　oscillations　in　a　pair　of　first-order　asymmetric　nonlinear　circuit　systems　are　developed　for　the　first　time.　The　purpose　of　this　study　is　to　show　the　paired　asymmetrical　nonlinear　oscillations　existing　in　paired　asymmetric　nonlinear　systems.　Such　analytical　solutions　in　nonlinear　systems　can　be　realized　through　the　nonlinear　circuit　systems.　Thus,　the　paired　nonlinear　electrical　circuits　are　established　for　the　experimental　study　of　the　periodic　oscillations.　The　analytical　paired　asymmetric　periodic　oscillations　are　regenerated　experimentally　through　the　paired　nonlinear　electrical　circuits.　The　analytical　and　experimental　periodic　oscillations　match　very　well.　The　accurate　analytical　solutions　of　periodic　oscillations　are　given　herein　in　time　and　frequency　domains.　To　consider　excitation　effects　on　periodic　oscillations　in　such　1-dimensional　nonlinear　circuit　systems,　the　asymmetric　periodic　oscillations　varying　with　excitation　amplitudes　for　the　nonlinear　circuit　are　presented　through　harmonic　amplitudes,　and　the　corresponding　stability　and　bifurcations　of　such　paired　asymmetric　periodic　oscillations　are　determined　through　eigenvalue　analysis.　Such　studies　provide　a　theoretic　base　to　design　the　nonlinear　circuit　devices　or　cells.　From　the　analytical　solutions,　the　experimental　and　numerical　results　are　carried　out　for　comparison　to　the　analytical　results.　Such　1-dimensional　first-order　nonlinear　electrical　circuit　devices　can　be　designed　for　extensive　applications　in　industry.　©　2022　Elsevier　Ltd