The irregular growth dynamics of the so-called locked (tilted) lamellar eutectic grains that are observed in directional solidification of nonfaceted/nonfaceted eutectic alloys, is attributable to a strong surface tension anisotropy of the interphase boundaries, which enters into the local-equilibrium (Young-Herring) condition at the trijunctions of the solid-liquid interfaces. Based on real-time observations of locked eutectic growth in thin samples, we propose that the lamellar tilt angle is selected by the system in such a way that the Hoffmann-Cahn surface tension force ((sigma) over right arrow vector) of the interphase boundaries is approximatively perpendicular to the solidification front.