In　this　paper,　we　propose　two　reconfigurable　intelligent　surface-aided　M-ary　frequency-modulated　differential　chaos　shift　keying　(RIS-M-FM-DCSK)　schemes.　In　scheme　I,　the　RIS　is　regarded　as　a　transmitter　at　the　source　to　incorporate　the　M-ary　phase-shift-keying　(M-PSK)　symbols　into　the　FM　chaotic　signal　and　to　reflect　the　resultant　M-ary　FM　chaotic　signal　toward　the　destination.　The　information　bits　of　the　source　are　carried　by　both　the　positive/negative　state　of　the　FM　chaotic　signal　and　the　M-PSK　symbols.　In　scheme　II,　the　RIS　is　treated　as　a　relay　so　that　both　the　source　and　relay　can　simultaneously　transmit　their　information　bits　to　the　destination.　The　information　bits　of　the　source　and　relay　are　carried　by　the　positive/negative　state　of　the　FM　chaotic　signal　and　M-PSK　symbols　generated　by　the　RIS,　respectively.　The　proposed　RIS-M-FM-DCSK　system　has　an　attractive　advantage　that　it　does　not　require　channel　state　information　for　detection,　thus　avoiding　complex　channel　estimation.　Moreover,　we　derive　the　theoretical　expressions　for　bit　error　rates　(BERs)　of　the　proposed　RIS-M-FM-DCSK　system　with　both　scheme　I　and　scheme　II　over　multipath　Rayleigh　fading　channels.　Simulations　results　not　only　verify　the　accuracy　of　the　theoretical　derivations,　but　also　demonstrate　the　superiority　of　the　proposed　system.　The　proposed　RIS-M-FM-DCSK　system　is　a　promising　low-cost,　low-power,　and　high-reliability　alternative　for　wireless　communication　networks.