The possibility of the high spin stable states in the Boron-Carbon layered network systems have theoretically investigated through several BC 6MR polyacene clusters. The HF/6-31G** calculations reveal that the alternant BC-benzene gives a quartet stable state rather than a doublet one, while a doublet state is more stable for the non-alternant BC-benzenes. Similarly, alternant BC-naphthalene gives a high-spin stable state (sextet) rather than lower ones (doublet, or quartet). These features are well understood by extending the Longuet-Higgins [l] theory to this BC system.