  We show that 1:1 ordering of A$'$ and A$''$ cations in
A$'_{1/2}$A$''_{1/2}$B$_2$X$_4$ magnetic spinels results in appearance of
magnetoelectric properties. Possible value of magnetically induced electric
polarization is calculated using the recently proposed microscopic model, which
takes into account spin-dependent electric dipole moments of magnetic ions
located in noncentrosymmetric crystallographic positions. We build
phenomenological models of magnetic phase transitions in cation-ordered
spinels, which describe ferromagnetic and antiferromagnetic ordering patterns
of B cation spins, and calculate the respective magnetoelectric responses. We
find that magnetoelectric coefficients diverge at ferromagnetic or weak
ferromagnetic phase transitions in ordered spinels.
