Abstract <p>The study describes the unusual auxetic and magnetostrictive behavior of binary iron-based alloys: galfenol Fe_{100 – <i>x</i>}Ga_<i>x</i> and alfenol Fe_{100 – <i>x</i>}Al_<i>x</i>. We present experimental and theoretical results explaining the intrinsic auxetic properties of galfenol and alfenol in the range 0 &lt; <i>x</i> &lt; 27.2. Theoretical conditions for achieving negative Poisson’s ratios in body-centered cubic metals are presented, along with calculated values of Poisson’s ratios and Young’s moduli for galfenol and alfenol as functions of the atomic percent of Ga and Al incorporated into the iron alloy matrix. The study attributes the negative Poisson’s ratios to elastic anisotropy, that is, the difference between the tetragonal <i>C</i> ' and rhombohedral <i>C</i>₄₄ elastic moduli in a cubic single crystal. Experimental results on the anisotropic magnetostrictive behavior of galfenol and alfenol are described as a function of the applied magnetic field direction. Concentration dependences of tetragonal and rhombohedral magnetostriction for galfenol are provided. The study associates the unusual behavior in a magnetic field with differences in the phase composition of the alloys. Magnetoelastic behavior is examined, and correlations between the elastic moduli <i>C</i>₁₁, <i>C</i>₁₂, <i>C</i>₄₄, the magnetoelastic constants <i>b</i>₁ and <i>b</i>₂, and the magnetostriction λ in cubic crystals are identified.</p>