  We present the first study of the QCD corrections to the color-singlet (CS)
$J/\psi$ production in deeply inelastic $ep$ scattering at HERA. The $K$-factor
ranges from $0.85$ to $2.38$ in the kinematic regions we study. In low
transverse momentum regions, the $K$-factors is even smaller, and close to 1,
which indicates good convergence of the perturbative expansion. With the QCD
corrections, the CS cross section is still below the data. At least at QCD
next-to-leading order, the color-octet mechanism is necessary to describe the
data.
