In an exploratory feasibility study we have measured the angular correlation between Auger electrons that were emitted in a cascadelike decay process after resonant photoexcitation, using synchrotron radiation from the Brookhaven National Synchrotron Light Source. While the monochromator was tuned to the argon $1\stackrel{\ensuremath{\rightarrow}}{s}4p$ resonance (3203.5 eV) we recorded Ar $\mathrm{LMM}$ Auger electrons in coincidence with ${\mathrm{KL}}_{2,3}{L}_{2,3}{,KL}_{1}{L}_{2,3},$ and ${\mathrm{KL}}_{2,3}{M}_{1,2,3}$ Auger electrons. We found different nonisotropic angular correlations between distinct energy regions of the $\mathrm{LMM}$ group of Auger lines and the ${\mathrm{KL}}_{2,3}{L}_{2,3}$ Auger electrons, while for other kinetic energies the $\mathrm{LMM}$ Auger electrons exhibit isotropy. Because the $\mathrm{KLL}$ and $\mathrm{LMM}$ Auger energies are so different, we believe that the nonisotropic angular correlation observed is due to an alignment effect rather than a dynamical postcollision interaction effect.