This paper investigates the possibility that interstellar turbulence is caused by nonlinear interactions among shear Alfvén waves. The authors focus on the symmetric case where oppositely directed waves carry equal energy fluxes, which excludes the solar wind where the outward flux significantly exceeds the ingoing one. They derive a theory for strong turbulence of shear Alfvén waves, showing that the inertial-range energy spectrum exhibits a critical balance between linear wave periods and nonlinear turnover timescales. The "eddy" structures are elongated in the direction of the magnetic field, with the parallel and perpendicular components of the wave vector related by $ k_{z} \approx k_{\perp}^{2/3} L^{-1/3} $, where $ L $ is the outer scale of the turbulence. The "one-dimensional" energy spectrum is proportional to $ k_{\perp}^{-5/3} $, an anisotropic Kolmogorov energy spectrum. Shear Alfvénic turbulence mixes specific entropy as a passive contaminant, leading to an electron density power spectrum that mimics the turbulence energy spectrum. Radio-wave scattering by these fluctuations produces anisotropic scatter-broadened images. Ion-neutral collisions restrict Alfvénic turbulence to highly ionized regions of the interstellar medium. The authors conclude that compressive MHD waves are not significantly generated by shear Alfvén waves in the critically balanced cascade. They also note that viscous and collisionless damping are unimportant in the interstellar medium. The paper supports the general picture of interstellar turbulence advanced by Higdon.This paper investigates the possibility that interstellar turbulence is caused by nonlinear interactions among shear Alfvén waves. The authors focus on the symmetric case where oppositely directed waves carry equal energy fluxes, which excludes the solar wind where the outward flux significantly exceeds the ingoing one. They derive a theory for strong turbulence of shear Alfvén waves, showing that the inertial-range energy spectrum exhibits a critical balance between linear wave periods and nonlinear turnover timescales. The "eddy" structures are elongated in the direction of the magnetic field, with the parallel and perpendicular components of the wave vector related by $ k_{z} \approx k_{\perp}^{2/3} L^{-1/3} $, where $ L $ is the outer scale of the turbulence. The "one-dimensional" energy spectrum is proportional to $ k_{\perp}^{-5/3} $, an anisotropic Kolmogorov energy spectrum. Shear Alfvénic turbulence mixes specific entropy as a passive contaminant, leading to an electron density power spectrum that mimics the turbulence energy spectrum. Radio-wave scattering by these fluctuations produces anisotropic scatter-broadened images. Ion-neutral collisions restrict Alfvénic turbulence to highly ionized regions of the interstellar medium. The authors conclude that compressive MHD waves are not significantly generated by shear Alfvén waves in the critically balanced cascade. They also note that viscous and collisionless damping are unimportant in the interstellar medium. The paper supports the general picture of interstellar turbulence advanced by Higdon.