In this study, we investigated the airy, cos-airy and cosh-airy beam lasers with optical vortex. Then, taking into account the Fourier transform, we examined and compared the propagation of these beams in a strong nonlinear system. The results indicated that by changing the input power p0 and the parameters b and the propagation length, the location of optical vortex displaces. It was shown that nonlinearity is one of the parameters that control optical vortex in optical systems used in these types of lasers. An important property in these beams is their direction variation due to the change in the mentioned parameters, which can be used in applications such as beam switching.