  Nonlinear equations of $p$-branes in $D=(2p+1)$-dimensional Minkowski space
are discussed. Presented are new exact solutions for a set of spinning
$p$-branes with $p=2,3,...,(D-1)/2$ and the Abelian symmetries $U(1)\times
U(1)\times... \times U(1)$ of their shapes.
