ON STRUCTURE EQUATIONS FOR SECOND ORDER CONNECTIONS E. Aguirre-Dab\'{a}n and I. S\'{a}nchez-Rodr\'{\i}guez Abstract. The basic facts concerning the structure equations of connections in the principal bundle of second order (holonomic) frames $F^2M$ on a differentiable manifold $M$ are presented here in a self contained and synthetic way. Advantage is taken from the embedding of $F^2M$ as a subset of $F(FM)$ and from viewing the group $ G^2(n)$ as a semidirect product. Keywords. Connections, frame bundles. MS classification. 53C.