In　this　paper,　we　study　a　local　stabilized　nonconforming　finite　element　method　for　the　generalized　Stokes　equations.　This　nonconforming　method　is　based　on　two　local　Gauss　integrals,　and　uses　the　equal　order　pairs　of　mixed　finite　elements　on　quadrilaterals.　Optimal　order　error　estimates　are　obtained　for　velocity　and　pressure.　Numerical　experiments　performed　agree　with　the　theoretical　results.　©　2012　Institute　for　Scientific　Computing　and　Information.