In this paper, we studied the canonical transformations of secondorder nonstandard generalized mechanics with exponential Lagrangians and Poisson theory on the first integrals. First, Hamilton principle of secondorder nonstandard generalized mechanics is established, the EulerLagrange equations are derived, the Hamiltonian is defined by using Legendre transformation, and the canonical equation are established. Secondly, the discriminant conditions of canonical transformation of secondorder nonstandard generalized mechanics are established, and four basic forms of canonical transformation are given by different choices of generating functions. Finally, the Lie algebraic structure of secondorder nonstandard generalized mechanics is verified, and Poisson theory of the first integral is established. Some examples are given to demonstrate the application of the results.