In this thesis we concentrate on finding tight upperbounds on the output error rate of concatenated coding systems with binary convolutional inner codes and Reed-Solomon outer codes. Performance of such a system can be estimated by first calculating the error rate of the inner code and then by evaluating the outer code performance. Two new methods are proposed to improve the classical union bound on convolutional codes. The methods provide better error estimates in the low signal-to-noise ratio (SNR) region where the union bound increases abruptly. An ideally-interleaved system performance is evaluated based on the convolutional code bit error rate estimates. Results show that having better estimates for the inner code performance improves the estimates on the overall system performance. For the analysis of a non-interleaved system, a new model based on a Markov Chain representation of the system is proposed. For this purpose, distribution of errors between the inner and outer decoding stages is obtained through simulation. Markov Chain parameters are determined from the error distribution and output error rate is obtained by analyzing the behavior of the model. The model estimates the actual behavior over a considerable SNR range. Extensive computer simulations are run to evaluate the accuracy of these methods.