Concentration and temperature transitions in strongly correlated Fe1-хCoxSi alloys with the Dzyaloshinsky-Moriyya (DM) interaction are considered within the framework of the spin-fluctuation theory and taking into account the results of LDA+U+SO calculations of the density of electronic states. It is shown that order-order concentration transitions with a change in the sign of the left-handed spin chirality (at x <0.2) to right-handed (at 0.2≤x<0.65), and again to left-handed, are associated with a change in the sign of the intermode interaction parameter. At the same time, it was indicated that in the region of compositions Fe1-хCoxSi 0.2≤x<0.65, temperature-prolonged first-order phase transitions appear, accompanied by the appearance of an intermediate temperature region of spin short-range order with uncompensated local magnetization and DM interaction. In an external magnetic field in this temperature range at 0.21-хCoxSi agree with the experiment.