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In structured light with controllable degrees of freedom (DoFs), the vortex beams carrying orbital angular momentum (OAM) give access to provide additional degrees of freedom for information transfer, and in classic field, the propagation invariant space time electromagnetic pulses are the possible approach to high dimensional states. This paper arose an idea that coupling the space polarization nonseparable states of vortex beams and space time nonseparable states of spatiotemporal pulse can generate numerous unique and beneficial effects. Here, we introduce an family of space time nonseparable electromagnetic vortices (STNEV). The pulses exhibit complex and robust spatiotemporal topological structure of the electromagnetic fields, multiple singularities in the Poynting vector maps and distributions of energy backflow. We apply a quantum-mechanics methodology for quantitatively characterizing space time nonseparability of the pulse. Our findings facilitate their applications in fields of information transfer, toroidal electrodynamics and inducing transient excitations in matter.