Twinned microstructure in CoPt and FePt alloys is formed in the process of atomic ordering at temperatures below T-K-temperature of the Al --> Ll(0) phase transformation. Polytwinned CoPt and FePt crystals consist of regular systems (blocks, plates, packets) of lamellar tetragonal crystallites of twin orientation called C domains. In our work, we determined the specific role of dispersity and the character of contact between the above structural elements in the formation of the magnetic domain structure (DS) and hysteresis properties of CoPt and FePt alloys. We showed that the magnetic DS of polytwinned crystals has a cooperative nature and consists of magnetic micro and macro domains. We constructed models of a cooperative DS and introduced the concept of a critical size of magnetic single-macrodomain structure of a polytwinned crystal (particle). We theoretically studied the quantitative relationship between the main parameters of the cooperative DS (width of macrodomains and the critical single-macrodomain size) and the thickness of C domains and the dimensions of plates and packets. The effect of the exchange and magnetostatic interactions (that arise at the twin boundaries of C domains) on the parameters of the DS are discussed and the results of a numerical calculation of hysteresis properties with allowance for these interactions are given. A conclusion is made that the exchange and magnetostatic interactions create additional metastable magnetic states in the twin system of lamellar crystallites with high uniaxial anisotropy. This leads to effective multiaxiality of the polytwinned crystals.