The author first deduces some algebraic properties of the \(r\)-th order quasijets, that are defined as certain linear morphisms between the \(r\)-times iterated tangent bundles in such a way that the classical \(r\)-jets and the nonholonomic \(r\)-jets form a special case of the quasijets. Then he generalizes the theory of nonholonomic higher order connections to the quasijet bundles. In particular, the second order connections are described in detail.