The surface behavior of spread sodium eicosanyl sulfate monolayers is characterized by determining the dilational moduli from different pi/A isotherms and from surface stress relaxation experiments in the short-time range (<10 min). The elasticities derived from the pi/A isotherms differ depending on the experimental conditions. The quasi-equilibrium isotherm displays a plateau in the range of coexistence of the condensed and the expanded phases and strong increases caused by the formation of a solid-like phase. In contrast, nonequilibrium pi/A isotherms yield effective elasticities showing a maximum within the phase coexistence range. The formation of a solid phase cannot be detected because of the onset of monolayer collapse. Different stress relaxation experiments were carried out for monolayer compression and dilation using transient drop volume jumps. Depending on the experimental run, these experiments lead to consistent and complementary results with those derived from pi/A isotherms under comparable conditions. The stress recoveries yield a relaxation time, a dilation viscosity, and a parameter characterizing the homogeneity of the relaxation process. The stress relaxation is interpreted accounting for both the nonequilibrium between the monolayer and the bulk phase and the nonequilibrium within the monolayer. The influence of alkylsulfate hydrolysis on the presented results was checked, It was found that within the time scale of the experiments no influence of hydrolysis could be detected.