Based on the generalized Huygens-Fresnel principle,taking the Laguer re-Gaussian (LG) beams as an example,the dynamic evolution and propagation trajectory of the higher-order coherent vorti ces and the higher-order optical vortices are studied in free space and atmospheric turbulence.The results show that the higher-order coherent vortices with topological charge of +m break down into m coherent vo rtices with topological charge of +1through propagation in free space and atmos pheric turbulence;the higher-order optical vortices are not broken down in free space,and the position of the high er-order optical vortices remains unchanged with the increase of propagation d istance;the higher-order optical vortices with top ological charge of +m break down into m ones with +1through propagation in atmospheric turbulence; both the pa rtial coherence of optical field and disturbance of atmospheric turbulence induce higher-order coherent vortices to break down.The se results will be beneficial for designing and developing the optical vortex co mmunication systems.