A search for squarks of R-parity violating supersymmetry is performed
in ep collisions at HERA using H1 1994 e(+) data. Direct single produc
tion of squarks of each generation by e(+)-quark fusion via a Yukawa c
oupling 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
art derived. At 95% confidence level, the existence of first generatio
n squarks is excluded for masses up to 240 GeV for coupling values lam
bda' greater than or similar to root 4 pi alpha(em). The limits obtain
ed 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' x cos theta(t) to e(+)d pair
s greater than or similar to 0.1 x root 4 pi alpha(em) where theta t i
s the mass mixing angle. Light stop squarks are furthermore searched f
or through pair production in (sic)-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' x cos theta
(t) > 10(-4).