This　paper　studies　the　parameter　identification　problem　for　a　large-scale　multivariable　systems.　In　terms　of　the　identification　obstacle　causing　by　huge　amounts　of　parameters　of　large-scale　systems,　a　separable　gradient　(synthesis)　identification　algorithm　is　developed　in　accordance　with　the　hierarchical　computation　principle.　For　the　large-scale　multivariable　equation-error　systems,　the　whole　parameters　are　detached　into　several　sub-parameter　matrices　based　on　the　scales　of　the　coefficient　matrices　of　the　inputs　and　outputs.　On　the　basis　of　the　detached　parameter　matrices,　multiple　parameter　estimation　sub-algorithms　are　presented　for　estimating　the　parameters　of　each　sub-matrix　through　using　the　gradient　search　and　multi-innovation　theory　from　real-time　measurements.　Concerning　the　problem　that　the　sub-algorithms　are　not　effective　because　of　the　unknown　parameters　existing　in　the　recursive　computation,　the　previous　estimates　of　the　unknown　parameters　and　the　interactive　estimation　are　introduced　into　the　sub-algorithms　to　eliminate　the　associated　items　that　make　the　sub-algorithms　impossible　to　implement.　In　order　to　analyze　the　convergence　of　the　proposed　algorithms　theoretically,　we　prove　the　convergence　by　using　martingale　convergence　theory　and　stochastic　principle.　Finally,　the　performance　tests　of　the　proposed　identification　approaches　for　large-scale　multivariable　systems　are　carried　out　on　several　numerical　examples　and　the　simulation　results　demonstrate　the　effectiveness　of　the　proposed　methods.　©　2023　Elsevier　B.V.