For systems displaying two-phase coexistence without rotational invariance, anisotropic surface tension and nonspherical droplets are present. To study small fluctuations around such droplets, we construct a natural coordinate system and find the quadratic form. In general, their spectrum differs from the isotropic case and affects the nature of the first-order transition singularities. However, in two bulk dimensions, the spectrum is sufficiently simple that the singularity is universal.