Mössbauer spectra and thermomagnetic curves for the Fe86−xMxZr7Nb2Cu1B4 (M = Co, Ni, CoCr, and Cr, x = 0 or 6) alloys in the as-quenched state and after the accumulative annealing in the temperature range 600–800 K for 10 min are investigated. The parent Fe86Zr7Nb2Cu1B4 amorphous alloy is paramagnetic at room temperature, and substitution of 6 at.% of Fe by Co, Ni, and CoCr changes the magnetic structure – the alloys become ferromagnetic, whereas replacing 6 at.% of Fe with Cr preserves the paramagnetic state. After the heat treatment at 600 K, the decrease of the average hyperfine field induction, as compared to the as-quenched state, is observed due to the invar effect. After this annealing, the Curie temperature for all investigated alloys decreases. The accumulative annealing up to 800 K leads to the partial crystallization; α-Fe or α-FeCo grains with diameters in the range of 12–30 nm in the residual amorphous matrix appear.