We consider the long-wavelength behavior of smectic liquid crystals (or any solid developing periodic order in only one direction) in the presence of anharmonic terms dictated by symmetry considerations. We analyze this anharmonic model of smectics with the use of analytic renormalization-group techniques directly in three dimensions. We find that the hydrodynamic description of smectics given by the harmonic theory is not valid at sufficiently small wave vectors. Instead, the elastic constants corresponding to the compression and undulation modes, respectively, vanish and diverge logarithmically at small wave vectors. Density correlations, which decay algebraically in the harmonic theory, are found to fall off with a distance-dependent power law at sufficiently long distances. Additionally, the system responds nonlinearly to applied stress at sufficiently small stress, i.e., Hooke's law is not valid. After presenting the calculations leading to the above results, we discuss the feasibility of experimental observation of these effects. © 1982 The American Physical Society.