  We study fractional branes in ${\CN}=2$ orbifold and ${\CN}=1$ conifold
theories. Placing a large number $N$ of regular D3-branes at the singularity
produces the dual ${\bf AdS}_5\times X^5$ geometry, and we describe the
fractional branes as small perturbations to this background. For the orbifolds,
$X^5={\bf S}^5/\Gamma$ and fractional D3-branes excite complex scalars from the
twisted sector which are localized on the fixed circle of $X^5$. The resulting
solutions are given by holomorphic functions and the field-theoretic
beta-function is simply reproduced. For $N$ regular and $M$ fractional
D3-branes at the conifold singularity we find a non-conformal ${\cal N}=1$
supersymmetric $SU(N+M)\times SU(N)$ gauge theory. The dual Type $\II$B
background is ${\bf AdS}_5\times {\bf T}^{1,1}$ with NS-NS and R-R 2-form
fields turned on. This dual description reproduces the logarithmic flow of
couplings found in the field theory.
