We studied the magnetostriction coefficients, λs, Curie temperature, Tc, and their dependence on annealing conditions in Fe47Ni27Si11B13C2 and Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 amorphous glass-coated microwires with rather different character of hysteresis loops. A positive λs ≈ 20 × 10−6 is observed in as-prepared Fe47Ni27Si11B13C2, while low and negative λs ≈ −0.3 × 10−6 is obtained for Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 microwire. Annealing affects the magnetostriction coefficients and Curie temperatures, Tc, of both Fe47Ni27Si11B13C2 and Co67Fe3.9Ni1.5B11.5Si14.5Mo1.6 glass-coated microwires in a similar way. Observed dependencies of hysteresis loops, λs and Tc on annealing conditions are discussed in terms of superposition of internal stresses relaxation and structural relaxation of studied microwires. We observed linear λs dependence on applied stress, σ, in both studied microwires. A decrease in the magnetostriction coefficient upon applied stress is observed for Co-rich microwires with low and negative magnetostriction coefficient. On the contrary, for Fe-Ni-rich microwires with a positive magnetostriction coefficient, an increase in the magnetostriction coefficient with applied stress is observed. The observed results are discussed considering the internal stresses relaxation and short range atomic rearrangements induced by annealing on hysteresis loops, magnetostriction coefficients and Curie temperatures of studied microwires.