Multimedia transmission over wired and wireless (hybrid) networks is increasingly needed as new services emerge and hybrid networks become more diverse and reliable. Quantifying quality of multimedia applications transmitted over hybrid networks is valuable for measuring network performance and its optimisation. For video, the process involves examining the images that make up the video, by quantifying distortion, noise, and complementing them with traffic parameters characterised by packet delay, delay variation (jitter) and percentage of packet loss ratio (%PLR). Processing all received packets to evaluate the quality of received application is computationally intensive. The study developed a new multi-input adaptive sampling method that allowed a subset of transmitted packets to be chosen according to variations in three synchronised traffic parameters inputs. The method integrated fuzzy logic and regression modelling of traffic parameters and adaptively adjusted the number of packets selected for processing. Statistical and neural networks methods were developed to evaluate quality of service (QoS) for video streaming and Voice over Internet Protocol (VoIP) transmitted over hybrid networks. The traffic parameters for QoS evaluations were delay, jitter and %PLR. The work involved, Bayesian classification and probabilistic neural network (PNN) based methods to process traffic parameters. QoS. This allocation conformed to the International Telecommunication Union (ITU) recommendations. Overall, the performance of Bayesian method was better than PNN when determining QoS for VoIP. In addition, the developed methods were successfully used in practical tests to analyse QoS in the wireless standards IEEE 802.11ac and IEEE 802.11n. QoS reflects provides information that indicates the extent the traffic parameters for an application are within the expected bounds. However, the user's perception of the received application is also relevant. This evaluation can be performed through quality of experience (QoE) analysis. For video, QoE considers issues such as image distortion and noise that in this study were quantified by structural similarity index measure (SSIM), peak signal to noise ratio (PSNR) and image difference (ID). A modular fuzzy logic-based system that individually determined QoS and QoE, then combined them to determine the overall quality of a wirelessly transmitted video was developed. The performance of the devised video quality evaluation system was compared against the subjective evaluation performed by 25 participants (i.e. mean opinion scores) and consistent results were observed. A further evaluation of the video quality evaluation system was carried by comparing its results against a recently reported video quality assessment method known as the spatial efficient entropic variation quality assessment. Again, comparable results were obtained between the two methods. The QoE evaluations were carried out both in a network laboratory and over an institutional network. The study resulted in development a multi-input adaptive sampling method and artificial intelligence and statistical based QoS and QoE evaluation methods. The proposed schemes improved the QoS and QoE assessments for multimedia applications. The devised adaptive sampling model in comparison with random, stratified and systematic non-adaptive sampling methods was more effective as it represented the traffic more precisely. The developed two probabilistic QoS methods showed consistency in their classifications. Both models successfully classified the received VoIP packets into their corresponding low, medium, and high QoS types. Furthermore, QoE with image partitioning approach has improved QoE evaluation as partitioned image approach provided more accurate results than full image approach. The proposed integration approach of three multimedia parameters SSIM, PSNR and ID improved accuracy of overall QoE assessments compared to single parameter approaches.