In this paper, we study ciphertext-only cryptanalysis of a cascade of pseudorandom sequence generators employing linear feedback shift registers (LFSRs) with so-called irregular clocking. The cascade of LFSRs is a well-known pseudorandom generator scheme that produces sequences with good cryptographic characteristics (long period, high linear complexity, good statistical properties, etc.) A method of cryptanalysis of cascades containing two such LFSRs is well known. We generalize this method to cryptanalysis of a cascade with an arbitrary number of LFSRs. We reconstruct a set of candidate clock control sequences at each stage of the cascade, instead of enumerating all the possible initial states of the corresponding subcascade. The reconstruction is performed by means of an independent search through the edit distance matrix associated with every stage of the cascade. The experimental results show that such a generalized method of cryptanalysis is feasible. This topic is of great significance to the study of the security of such schemes applied to digital communications of cross-border e-commerce.