  In this note we construct Mabuchi $\mathcal{L}^{{\rm M}}_{\omega}$ functional
and Aubin-Yau functionals $\mathcal{I}^{{\rm AY}}_{\omega}, \mathcal{J}^{{\rm
AY}}_{\omega}$ on any compact complex surfaces, and establish a number of
properties. Our construction coincides with the original one in the K\"ahler
case.
