Development　of　fair　and　efficient　algorithms　for　resource　allocation　to　secondary　users　(SUs)　is　one　of　the　key　issues　in　the　design　of　cognitive　radio　(CR)　systems.　In　this　paper,　we　present　a　two-step　resource　allocation　solution　for　multiuser　based　CR　systems　employing　orthogonal　frequency　division　multiplexing　(OFDM).　The　solution　allocates　the　subcarriers　to　SUs　in　the　first　step,　considering　proportional　fairness.　In　the　second　step,　the　solution　allocates　the　power　to　the　subcarriers　to　maximize　sum　capacity　of　all　SUs,　without　causing　excessive　interference　to　the　primary　users　(PUs).　Simulation　results　and　performance　analysis　show　that　our　proposed　solution　can　offer　a　beneficial　efficiency-versus-fairness　tradeoff,　while　largely　reducing　computation　cost　compared　to　the　existing　solution.　©　2010　IEEE.