The paper considers the problem of sensitivity of large precision space structures made of high-modulus fibrous polymer composite materials to external and internal microdynamic effects. This problem is related to the extent of structure forming elements, as well as to an abrupt increase in the elastic modulus of the material when passing the threshold of low stresses. It is found that under low loading in the orbital flight conditions the calculated values of the elastic modulus of large precision space structures made of high-modulus fibrous polymer composite materials may be higher than the real ones by more than 20 times, which must be taken into account in the calculations. Possible ways to reduce the sensitivity of such space structures made of high-modulus fibrous polymer composite materials to external and internal microdynamic effects are shown.