  Measurements are presented of $K^0$ meson and $\Lambda$ baryon production in
deep-inelastic positron-proton scattering (DIS) in the kinematic range $10 <
Q^2 < 70 $GeV$^2$ and $10^{-4} < x < 10^{-2}$. The measurements, obtained using
the H1 detector at the HERA collider, are discussed in the light of possible
mechanisms for increased strangeness production at low Bjorken-$x$. Comparisons
of the $x_F$ spectra, where $x_F$ is the fractional longitudinal momentum in
the hadronic centre-of-mass frame, with results from electron-positron
annihilation are made. The $x_F$ spectra and the $K^0$ ``seagull'' plot are
compared with previous DIS results. The mean $K^0$ and $\Lambda$ multiplicities
are studied as a function of the centre-of-mass energy $W$ and are observed to
be consistent with a logarithmic increase with $W$ when compared with previous
measurements. A comparison of the levels of strangeness production in
diffractive and non-diffractive DIS is made. An upper limit of $0.9 $nb, at the
95% confidence level, is placed on the cross-section for QCD instanton induced
events.
