  In this paper, we compute the first set of ${\cal O}(\alpha_s^2)$ corrections
to semi-inclusive deep inelastic scattering structure functions. We start by
studying the impact of the contribution of the partonic subprocesses that open
at this order for the longitudinal structure function. We perform the full
calculation analytically, and obtain the expression of the factorized cross
section at this order. Special care is given to the study of their flavour
decomposition structure. We analyze the phenomenological effect of the
corrections finding that, even though expected to be small a priori, it turns
out to be sizable with respect to the previous order know, calling for a full
NNLO calculation.
