A family of Majumdar-Papapetrou type solutions in σ -model of p -brane origin is obtained for all direct sums of finite-dimensional simple Lie algebras. Several examples of p -brane dyonic configurations in D = 10 (IIA) and D = 11 supergravities corresponding to the Lie algebra A 2 are considered.

Black p-brane solutions for a wide class of intersection rules and Ricci-flat "internal" spaces are considered. They are defined up to moduli functions H s obeying non-linear differential equations with certain boundary conditions imposed. A new solution with intersections corresponding to the Lie algebra A 3 is obtained. The functions H 1 , H 2 and H 3 for this solution are polynomials of degree 3, 4 and 3, correspondingly. An example of A 3 -solution with three 3-branes in 12-dimensional model (suggested by N. Khviengia et al) is presented.

Black p-brane solutions for a wide class of intersection rules and Ricci-flat "internal" spaces are considered. They are defined up to moduli functions H s obeying non-linear differential equations with certain boundary conditions imposed. A new solution with intersections corresponding to the Lie algebra A 3 is obtained. The functions H 1 , H 2 and H 3 for this solution are polynomials of degree 3, 4 and 3, correspondingly. An example of A 3 -solution with three 3-branes in 12-dimensional model (suggested by N. Khviengia et al) is presented.