| Summary: | <p>The production of the neutral strange particles Λ, Λ[bar] and <em>K<sup>0</sup><sub>s</sub></em> at HERA has been studied with the ZEUS detector, using an integrated luminosity of 121<em>pb</em><sup>-1</sup> . Differential cross-sections are measured in a High <em>Q</em><sup>2</sup> DIS sample (<em>Q</em><sup>2</sup> ≥ 25GeV<sup>2</sup>), a Low <em>Q</em><sup>2</sup> DIS sample (5 ≤ <em>Q</em><sup>2</sup> ≤ 25GeV<sup>2</sup> ) and a photoproduction sample. The photoproduction sample has <em>Q</em><sup>2</sup> <= 1GeV<sup>2</sup> and at least two jets that satisfy <em>E<sub>T</sub><sup>jet</sup></em> > 5GeV and |<em>η<sup>jet</sup></em>| < 2.4. Cross-sections are measured as a function of the particle <em>P<sub>T</sub></em> and <em>η</em>, and additionally as a function of the event <em>Q</em><sup>2</sup> and <em>x</em> in the DIS samples, and as a function of <em>x<sub>γ</sub></em> in the photoproduction sample. The DIS cross-sections are compared to the ARIADNE Monte Carlo, which broadly describes the data. The photoproduction cross-sections are compared to PYTHIA, where the agreement is less good, particularly at low <em>x<sub>γ</sub></em>. The baryon-antibaryon asymmetry, defined as (Λ-Λ[bar])/(Λ+Λ[bar]), is measured and always found to be consistent with zero, indicating little transfer of the Baryon Number from the beam proton to the Λ system in the detector region. The polarization of Λ and Λ[bar] is measured and also found to be always consistent with zero, indicating that there is no preferred frame in Λ production. The baryon-meson ratio (Λ + Λ[bar])/<em>K<sup>0</sup><sub>s</sub></em> is studied, and is found to generally agree with ARIADNE in DIS, but give an excess over PYTHIA in photoproduction. The excess is particularly prominent at low <em>x<sub>γ</sub></em> in events with no clear jet structure. This is interpreted as hadron production in this region depending on a more-than-one-dimensional overlap of quark wave functions. An excess of strangeness in this region at low <em>x<sub>γ</sub></em> with no high <em>E<sub>T</sub></em> jets would be significant. It is investigated by taking the ratio of strange particles to charged tracks but no excess is seen.</p>
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