Fundamental laws and balance equations as well as C-D inequalities in conti
nuum mechanics are carefully restudied, incompleteness of existing balance
laws of angular momentum and conservation laws of energy as well as C-D ine
qualities are pointed out, and finally new and more general conservation la
ws of energy and corresponding balance equations of energy as well as C-D i
nequalities in local and nonlocal asymmetric continua are presented.