  A search for leptoquarks at HERA was performed in H1 using 1994 $e^+ p$ data
corresponding to an integrated luminosity of about $3 \pb^{-1}$. Single
leptoquarks were searched for in direct positron-quark fusion processes taking
into account possible decays into lepton-quark pairs of either the first, the
second, or the third generation. No significant deviation from the Standard
Model predictions is found in the various final states studied and mass
dependent exclusion limits are derived on the Yukawa couplings of the
leptoquarks. Compared with earlier results from an analysis of $e^-p$ data,
exclusion limits are considerably improved for leptoquarks which could be
produced via $e^+$-{\it valence~quark} fusion. For leptoquarks with lepton
flavour conserving couplings, masses up to $275 \GeV$ (depending on the
leptoquark type) are excluded for coupling values larger than $\sqrt{ 4 \pi
\alpha_{em}}$. For leptoquarks with lepton flavour violating couplings, masses
up to $225 \GeV$ are excluded for the first time in a direct search for
couplings with leptons of the second or third generation larger than $\sqrt{ 4
\pi \alpha_{em}}$. Fourteen possible combinations of couplings are studied and
stringent exclusion limits comparable or better than any existing direct or
indirect limits are obtained for each leptoquark type.
