This paper presents an operational reconstruction technique of most stream ciphers. We primarily expose it for key-stream generators which consist of several linear feedback shift registers combined by a nonlinear Boolean function. It is shown how to completely recover the different feedback polynomials and the combining function, when the algorithm is totally unknown. This attack only requires the knowledge of some ciphertexts, which may be generated from different secret keys. Estimates of necessary ciphertext length and experimental results are detailed.