Simultaneous multi-slice (SMS) MRI allows for the acquisition of several slices at the same time. We propose a novel reconstruction technique for radial SMS MRI based on Regularized Nonlinear Inversion (NLINV). This method does not require a priori knowledge of the coil sensitivities. We present the simultaneous estimation of images and coil sensitivities of two slices of a phantom from 10-fold undersampled data. Image quality is analyzed for different sampling schemes and compared to single-slice acquisitions. Clinical relevance is demonstrated by in-vivo imaging of two slices of a human heart in real-time at a time-resolution of 30.8 ms per frame.