  A search for squarks of R-parity violating supersymmetry is performed in $ep$
collisions at HERA using H1 1994 $e^+$ data. Direct single production of
squarks of each generation by $e^+$-quark fusion via a Yukawa coupling
$\lambda'$ is considered. All possible R-parity violating decays and gauge
decays of the squarks are taken into account. No significant deviation from the
Standard Model predictions is found in the various multi-lepton and multi-jet
final states studied and exclusion limits are derived. At 95% confidence level,
the existence of first generation squarks is excluded for masses up to $240
\GeV $ for coupling values $\lambda' \gtrsim \sqrt{4\pi \alpha_{em}}$.The
limits obtained are shown to be only weakly dependent on the free parameters of
the Minimal Supersymmetric Standard Model. Stop squarks are excluded for masses
up to $138 \GeV$ for coupling $\lambda' \times \cos \theta_t$ to $e^+d$ pairs
$\gtrsim 0.1 \times \sqrt{4\pi \alpha_{em}}$, where $\theta_t$ is the mass
mixing angle. Light stop squarks are furthermore searched for through pair
production in $\gamma$-gluon fusion processes. No signal is observed and
exclusion limits are derived. Masses in the range 9 to $24.4 \GeV$ are excluded
at 95% confidence level for $\lambda' \times \cos \theta_t > 10^{-4}$.
