First results on inclusive D0 and D* production in deep inelastic $ep$ scattering are reported using data collected by the H1 experiment at HERA in 1994. Differential cross sections are presented for both channels and are found to agree well with QCD predictions based on the boson gluon fusion process. A charm production cross section for 10GeV$~2\le Q~2\le100$GeV$~2$ and $0.01\le y\le0.7$ of $\sigma\left(ep\rightarrow c\overlinecX\right) = (17.4 \pm 1.6 \pm 1.7 \pm 1.4)$nb is derived. A first measurement of the charm contribution F2_charm(x,Q~2) to the proton structure function for Bjorken $x$ between $8\cdot10~{-4}$ and $8\cdot10~{-3}$ is presented. In this kinematic range a ratio F2_charm/F2= 0.237\pm0.021{+0.043\atop-0.039}$ is observed.
The inclusive production of D^{*+-}(2010) mesons in deep-inelastic scattering is studied with the H1 detector at HERA. In the kinematic region 1<Q^2<100 GeV^2 and 0.05<y<0.7 an e^+p cross section for inclusive D^(*+-) meson production of 8.50+- 0.42 (stat.)^(+1.21)_(-1.00) (syst.) nb is measured in the visible range p_(tD^*)>1.5 GeV and |\eta_(D^*)|<1.5. Single and double differential inclusive D^(*+-) meson cross sections are compared to perturbative QCD calculations in two different evolution schemes. The charm contribution to the proton structure, F_2^c(x,Q^2), is determined by extrapolating the visible charm cross section to the full phase space. This contribution is found to rise from about 10% at Q^2 = 1.5 GeV^2 to more than 25% at Q^2 = 60 GeV^2 corresponding to x values ranging from 5*10^(-5) to 3*10^(-3)$.