Full-duplex (FD) systems have been introduced to provide high data rates for beyond fifth-generation wireless networks through simultaneous transmission of information over the same frequency resources. However, the operation of FD systems is practically limited by the self-interference (SI), and efficient SI cancelers are sought to make the FD systems realizable. Typically, polynomial-based cancelers are employed to mitigate the SI; nevertheless, they suffer from high complexity. This article proposes two novel hybrid-layers neural network (NN) architectures to cancel the SI with low complexity. The first architecture is referred to as hybrid-convolutional recurrent NN (HCRNN), whereas the second is termed as hybrid-convolutional recurrent dense NN (HCRDNN). In contrast to the state-of-the-art NNs that employ dense or recurrent layers for SI modeling, the proposed NNs exploit, in a novel manner, a combination of different hidden layers (e.g., convolutional, recurrent, and/or dense) in order to model the SI with lower computational complexity than the polynomial and the state-of-the-art NN-based cancelers. The key idea behind using hybrid layers is to build an NN model, which makes use of the characteristics of the different layers employed in its architecture. More specifically, in the HCRNN, a convolutional layer is employed to extract the input data features using a reduced network scale. Moreover, a recurrent layer is then applied to assist in learning the temporal behavior of the input signal from the localized feature map of the convolutional layer. In the HCRDNN, an additional dense layer is exploited to add another degree of freedom for adapting the NN settings in order to achieve the best compromise between the cancellation performance and computational complexity. Complexity analysis and numerical simulations are provided to prove the superiority of the proposed architectures.