  We study brane configurations for four dimensional N=1 supersymmetric gauge
theories with quartic superpotentials which flow in the infrared to manifolds
of interacting superconformal fixed points. We enumerate finite N=2 theories,
from which a large class of marginal N=1 theories descend. We give the brane
descriptions of these theories in Type IIA and Type IIB string theory. The Type
IIB descriptions are in terms of D3 branes in orientifold and generalized
conifold backgrounds. We calculate the Weyl and Euler anomalies in these
theories, and find that they are equal in elliptic models and unequal in a
large class of finite N=2 and marginal N=1 non-elliptic theories.
