A　new　structure　and　macromodeling　approach　which　is　an　advance　over　high-order　recurrent　neural　network　named　bidirectional　high-order　deep　recurrent　neural　network　(BIHODRNN)　is　proposed　in　this　paper　for　the　first　time　for　nonlinear　circuits.　In　the　proposed　structure,　besides　the　fully　connected　weights　to　the　neurons　of　multiple　previous　time　steps　of　the　same　hidden　layer　in　conventional　high-order　recurrent　neural　network　(HORNN),　there　are　additional　fully　connected　weights　to　the　neurons　of　that　hidden　layer　for　multiple　next　times　steps.　Due　to　more　training　parameters　compared　to　conventional　RNN　and　HORNN,　the　proposed　BIHODRNN　can　train　and　predict　more　complex　relationships　in　a　faster　and　more　efficient　way　and　can　better　capture　long-term　dependencies.　Also,　because　of　bidirectional　structure　with　multiple　orders　to　the　next　time　steps,　it　can　predict　the　output　signals　beyond　the　training　time　intervals　with　much　better　accuracy.　To　improve　the　accuracy　of　the　proposed　BIHODRNN　even　more,　another　structure　and　method　called　Hybrid　BIHODRNN　was　presented　in　this　paper.　By　combining　layers　of　different　orders　and　different　directionality　in　Hybrid　BIHODRNN,　the　training　parameters　are　significantly　decreased　leading　to　the　reduction　of　overfitting　problem　and　increasing　the　model　accuracy.　Furthermore,　the　proposed　BIHODRNN　and　its　hybrid　version　need　smaller　number　of　training　data　compared　to　the　HODRNN　for　generating　a　model　with　similar　accuracy.　Moreover,　two　proposed　approaches　are　notably　faster　than　the　transistor-level　models　in　circuit　simulators　for　acquiring　similar　accuracy.　The　superiorities　of　the　proposed　approaches　are　investigated　by　modeling　two　nonlinear　circuit　examples,　namely,　5-coupled　and　3-coupled　line　high-speed　interconnects　both　driven　by　a　four-stage　driver.　IEEE