Appetizing solid composition of the medicinal, nutraceutical or nutritional supplement type, for oral administration to mammals, except man, in particular for the pet such as dog, cat or horse, which comprises with respect to the total weight of the composition : - from 5 to 30%, preferably from 8 to 20% by weight of at least one fatty material, selected from a liquid oil, a fatty body, a wax or a mixture of these, the liquid oil not being able to represent more from 8% by weight of the composition, - from 0.001 to 55% by weight of at least one active substance, and - from 20 to 95%, preferably from 40 to 70% by weight of at least one palatable material, characterized because: a) liquid oil is selected from olive oil, peanut oil, rapeseed oil, sunflower oil, and mixtures thereof； b) the fatty body is selected from chicken fat, duck fat, lard, tallow, butter, palm fat, palmitic stearin, margarine, eventually hydrogenated palm oil, cetyl palmitate, hydrogenated coconut oil and mixtures thereof； c) the wax is selected from beeswax, carnauba wax, candelilla wax, and mixtures thereof； d) the desirable matter is selected from meat, meat meal, fish meal, cheese powder, milk products, liver powder, gelatin, extracts of these animal substances or their derivatives ； the brewer's yeast； plant fibers； vegetable products or by-products such as fenugreek, apple, carrot, fodder beet, sugar beet, thyme, alfalfa, sugarcane, cereals such as oats, wheat, rice and corn, soybeans, their derivatives such as flours, and mixtures thereof； crystallized sucrose, powder, glucose, invert sugar, molasses, honey or its derivatives； and their mixtures； or the sodium chloride, and e) said solid composition is obtained by mixing the components, vaporization of the fat, calibration of the dry and fluid granulate, and compression of the granulate with a broth cube press, in which - the mixture It is presented in the form of a homogeneous, dry, fluid granulate, - the dry and fluid granulate has a gra
