In this note we construct a new class of superconformal field theories as m
ass deformed N=4 super Yang-Mills theories. We will argue that these theori
es correspond to the fixed points which were recently found [1] studying th
e deformations of the dual IIB string theory on AdS(5) X S-5. (C) 1999 Publ
ished by Elsevier Science B.V. All rights reserved.