  Searches at the e-p collider HERA for supersymmetric partners of the Standard
Model fermions are presented. Assuming R-parity conservation, selectrons and
squarks of the Minimal Supersymmetric Standard Model are excluded for masses up
to 65 GeV in a new region of the standard parameter space. Admitting in
addition a R-parity violating Yukawa coupling $\lambda'$, squarks are sought
through direct e-q fusion in a yet unexplored mass-coupling domain, taking into
account all possible squark decays. Squark masses up to 240 GeV are excluded
for $\lambda' \gtrsim \sqrt{4 \pi \alpha_{em}}$, depending only weakly on the
free model parameters.
