According to this article in Playbill:

It was a good day for the Boys of Broadway. HISTORY BOYS by Alan Bennett and JERSEY BOYS won the Drama League Awards for Outstanding Play and Outstanding Musical.

The Lincoln Center Theatre production of Odet's Awake and Sing and the John Doyle staging of Sondheim's SWEENEY TODD got the nods for Outstanding Revival of a Play and Musical, respectively.

Christine Ebersole took the prize for Distinguished Performances for her work playing two roles in the Off-Broadway musical Grey Gardens.

The Drama League revealed the winners for its 2006 awards at its annual gala luncheon. Alan Cumming, who is currently in the Broadway revival of The Threepenny Opera, hosted the annual event.

The complete 2006 nominations are (with winners in boldface):

DISTINGUISHED PRODUCTION OF A MUSICAL
The Color Purple
The Drowsy Chaperone
Grey Gardens
Jersey Boys
[title of show]
See What I Wanna See
The Wedding Singer

DISTINGUISHED PRODUCTION OF A PLAY
Dedication, or the Stuff of Dreams
History Boys
The Lieutenant of Inishmore
Stuff Happens
Measure for Pleasure
Rabbit Hole
The Ruby Sunrise
Spirit

DISTINGUISHED REVIVAL OF A MUSICAL
Jacques Brel Is Alive and Well and Living in Paris
The Pajama Game
Sweeney Todd
The Threepenny Opera
Two Gentleman of Verona

DISTINGUISHED REVIVAL OF A PLAY
All's Well That Ends Well
Awake and Sing!
The Caine Mutiny Court-Martial
Celebration and the Room
Faith Healer
Landscape of the Body
A Soldier's Play
Three Days of Rain
The Trip to Bountiful

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