Gait speed is an important biomechanical determinant of gait patterns, with joint kinematics being influenced by it. This study aims to explore the effectiveness of fully connected neural networks (FCNNs), with a potential application for exoskeleton control, in predicting gait trajectories at varying speeds (specifically, hip, knee, and ankle angles in the sagittal plane for both limbs). This study is based on a dataset from 22 healthy adults walking at 28 different speeds ranging from 0.5 to 1.85 m/s. Four FCNNs (a generalised-speed model, a low-speed model, a high-speed model, and a low-high-speed model) are evaluated to assess their predictive performance on gait speeds included in the training speed range and on speeds that have been excluded from it. The evaluation involves short-term (one-step-ahead) predictions and long-term (200-time-step) recursive predictions. The results show that the performance of the low- and high-speed models, measured using the mean absolute error (MAE), decreased by approximately 43.7% to 90.7% when tested on the excluded speeds. Meanwhile, when tested on the excluded medium speeds, the performance of the low-high-speed model improved by 2.8% for short-term predictions and 9.8% for long-term predictions. These findings suggest that FCNNs are capable of interpolating to speeds within the maximum and minimum training speed ranges, even if not explicitly trained on those speeds. However, their predictive performance decreases for gaits at speeds beyond or below the maximum and minimum training speed ranges.