A magnetic response of the alkali-metal superoxides comes from the p-orbital S = 1/2 spins of anionic O2- molecules. As the O2- molecules are highly reorientable and the corresponding degenerate p orbitals are prone to orbital ordering, these structurally very simple systems exhibit surprisingly complex physics. In CsO2, the p-orbital ordering leading to the formation of spin-1/2 chains below 70 K and a subsequent low-temperature magnetic ordering below 10 K are well established, but the magnetic structure of the ordered phase remains unknown. In NaO2, our NMR results reveal a series of crossovers between different spin-fluctuating regimes below 180 K, but with no signs of magnetic ordering. To address different spin-fluctuating regimes in CsO2 and NaO2 and to unambiguously answer the questions of the existence of the low-temperature magnetic order in NaO2, we are proposing a muSR study.