The article analyzes the possibilities of measuring gradients of a magnetic field of high order. With increasing order of the gradiometer its sensitivity with unchanged overall dimensions is greatly reduced while the noiseproofness of a real gradiometer decreases at the same time. Besides that, the coefficient of transformation of a real gradiometer changes substantially under the effect of the stray field of the investigated source and of the gradients of this field of the preceding orders. Doubts are expressed as to the feasibility of gradiometers of higher orders.