  In this work we combine theory and experiment to study transient magnetic
circular dichroism (tr-MCD) in the extreme ultraviolet spectral range (XUV) in
bulk Co and CoPt. We use the \emph{ab-initio} method of real-time
time-dependent density functional theory (RT-TDDFT) to simulate the
magnetization dynamics in the presence of ultrafast laser pulses. From this we
demonstrate how tr-MCD may be calculated using an approximation to the
excited-state linear-response. We apply this approximation to Co and CoPt and
show computationally that element-specific dynamics of the local spin moments
can be extracted from the tr-MCD in XUV energy range, as is commonly assumed.
We then compare our theoretical prediction for the tr-MCD for CoPt with
experimental measurement and find excellent agreement at many different
frequencies including the $M_{2 3}$-edge of Co and $N_{6 7}$- and $O_{2 3}$-
edges of Pt.
