This　brief　deals　with　the　robust　filtering　problem　for　uncertain　linear　systems　with　delayed　states　and　outputs.　Both　time-invariant　and　time-varying　cases　are　considered.　For　the　time-invariant　case,　an　algebraic　Riccati　matrix　inequality　approach　is　proposed　to　design　a　robust　Hinfinity　filter　such　that　the　filtering　process　remains　asymptotically　stable　for　all　admissible　uncertainties,　and　the　transfer　function　from　the　disturbance　inputs　to　error　state　outputs　satisfies　the　prespecified　Hinfinity　norm　upper　bound　constraint.　We　establish　the　conditions　under　which　the　desired　robust　Hinfinity　filters　exist,　and　derive　the　explicit　expression　of　these　filters.　For　the　time-varying　case,　we　develop　a　differential　Riccati　inequality　method　to　design　the　robust　filters.　A　numerical　example　is　provided　to　demonstrate　the　validity　of　the　proposed　design　approach.