The paper deals with iterative decoding algorithms of low-density convolutional (LDC) codes. The authors analyse their asymptotic properties, discussing two families of LDC codes, namely homogeneous LDC codes and a convolutional version of turbo codes. They prove the existence of an upper bound on the decoding bit error probability and bounds on iterative limits for LDC codes and a family of turbo codes. They also discuss a derivation of these bounds. Procedures applied by the authors are analogous to those proposed by Gallager. Bounds on iterative limits are obtained for two channel models: the additive white Gaussian noise channel and the binary symmetric channel. For the calculation of estimates of log-likelihood ratios -- estimates of the Bhattacharyya parameter -- a Monte Carlo technique is used.