The system of two scalar order parameters on a complex scale-free network is analyzed in the spirit of Landau theory. To add a microscopic background to the phenomenological approach, we also study a particular spin Hamiltonian that leads to coupled scalar order behavior using the mean-field approximation. Our results show that the system is characterized by either of two types of ordering: either one of the two order parameters is zero or both are nonzero but have the same value. While the critical exponents do not differ from those of a model with a single order parameter on a scale-free network, there are notable differences for the amplitude ratios and the susceptibilities. Another peculiarity of the model is that the transverse susceptibility is divergent at all T
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