For diffusion measurements, stimulated-echo acquisition mode (STEAM) has been widely used. To enhance sensitivity to microstructure, previous studies used STEAM to vary the diffusion time by changing the mixing time tM. Here we show that varying tM results in an “apparent” STEAM-measured diffusivity dependence on tM, irrespective of genuine microstructure-specific time dependence. This effect is caused by T1-relaxation and water exchange between myelin water and "free" water (intra- and extra-axonal water). We propose a modified Kärger model considering diffusion+T1-relaxation+exchange, and demonstrate that exchange-induced tM-dependence explains ~20-50% of the total diffusion time dependence, and should be considered while using STEAM.