Two algorithms are presented for the generation of full-length shift-register cycles, also referred to as de Bruijn sequences. The first algorithm generates

full cycles of length

, using

bits of storage, where

is a free parameter in the range

, and

is of the order of

. The second algorithm generates about

full cycles of length

, using about

bits of storage. In both algorithms, the time required to produce the next bit from the last

bits is close to

. A possible application to the construction of stream ciphers is indicated.