Exhibit 99.1 Press release of the Registrant dated December 2, 1998.

FOR IMMEDIATE RELEASE

Contacts:  

   Media Contact:              Investor Contact:       Treasury Contact:
   Qwest Communications        Qwest Communications    Qwest Communications
   Christy Weiner              Lee Wolfe               Stephen H. Shoemaker
   (303) 992-2085              (800) 567-7296          (303) 992-2003
   christine.weiner@qwest.net  IR@qwest.net            steve.shoemaker@qwest.net


                   QWEST ANNOUNCES REDEMPTION OF SENIOR NOTES


DENVER,  December 2, 1998 - Qwest  Communications  International  Inc.  (Nasdaq:
QWST) today announced that it will redeem on December 31, 1998, $87.5 million of
its 10 7/8 percent Series B Senior Notes due 2007.  Bankers Trust  Company,  the
Trustee for the Notes,  issued the required  notice to affected  Noteholders  on
December 1, 1998.  Under the terms of the Indenture for the Notes,  dated August
28,  1997,  Qwest may redeem up to 35  percent,  or $87.5  million,  of the $250
million principal amount of the 10 7/8 percent Notes.

Robert  Woodruff,  executive vice president and chief financial  officer,  Qwest
Communications  said,  "The  redemption  of the Notes  strengthens  our  capital
structure and reflects  positively  on Qwest's  growth and ability to access the
capital markets on more favorable terms."

About Qwest
Qwest  Communications   International  Inc.  (NASDAQ:   QWST)  is  a  multimedia
communications  company  headquartered in Denver,  Colorado with more than 7,000
employees and over 80 sales offices  worldwide.  With its  world-class  data and
multimedia network,  marketing expertise, and customer care and billing systems,
Qwest is delivering high-quality data, video and voice connectivity securely and
reliably to  customers  around the world.  Further  information  is available at
www.qwest.net.