The production of neutral strange hadrons is investigated using deep-inelastic scattering events measured with the H1 detector at HERA. The measurements are made in the phase space defined by the negative four-momentum transfer squared of the photon $2 < Q^2 < 100 GeV^2$ and the inelasticity $0.1 < y < 0.6$. The $K_s$ and $\Lambda$ production cross sections and their ratios are determined. $K_s$ production is compared to the production of charged particles in the same region of phase space. The $\Lambda$ - anti-$\Lambda$ asymmetry is also measured and found to be consistent with zero. Predictions of leading order Monte Carlo programs are compared to the data.