Let　Gn　be　a　class　of　graphs　on　n　vertices.　For　an　integer　c,　let　ex　(Gn,　c)　be　the　smallest　integer　such　that　if　G　is　a　graph　in　Gn　with　more　than　ex　(Gn,　c)　edges,　then　G　contains　a　cycle　of　length　more　than　c.　A　classical　result　of　Erdös　and　Gallai　is　that　if　Gn　is　the　class　of　all　simple　graphs　on　n　vertices,　then　ex　(Gn,　c)　=　c/2　(n-1).　The　result　is　best　possible　when　n-1　is　divisible　by　c-1,　in　view　of　the　graph　consisting　of　copies　of　Kc　all　having　exactly　one　vertex　in　common.　Woodall　improved　the　result　by　giving　best　possible　bounds　for　the　remaining　cases　when　n-1　is　not　divisible　by　c-1,　and　conjectured　that　if　Gn　is　the　class　of　all　2-connected　simple　graphs　on　n　vertices,　then　ex(Gn,　c)　=　max　{f(n,　2,　c),　f(n,　⌊c/2⌋,　c)},　where　f(n,t,c)　=　(c+1-t　2)　+　t(n-c-1+t),　2　≤t≤c/2,　is　the　number　of　edges　in　the　graph　obtained　from　Kc+1-t　by　adding　n-(c+1-t)　isolated　vertices　each　joined　to　the　same　t　vertices　of　Kc+1-t.　By　using　a　result　of　Woodall　together　with　an　edge-switching　technique,　we　confirm　Woodall＇s　conjecture　in　this　paper.　©　2004　Elsevier　Inc.　All　rights　reserved.