  In the paper the Ising model with competing $J_1$ and $J_2$ interactions with
spin values $\pm 1$, on a Cayley tree of order 2 (with 3 neighbors) is
considered . We study the structure of the ground states and verify the Peierls
condition for the model. Our second result gives description of Gibbs measures
for ferromagnetic Ising model with $J_1<0$ and $J_2=0$, using a contour
argument which we also develop in the paper. By the argument we also study
Gibbs measures for a natural generalization of the Ising model. We discuss some
open problems and state several conjectures.\
