In this paper, we present two new normal forms for fuzzy linear grammars. Moreover, we introduce two new classes of fuzzy machines. The first is the class of fuzzy linear automata (FLA). We show that automata of this type is equivalent to the fuzzy linear grammar, i.e., we prove that the class of fuzzy languages is recognized by fuzzy linear automata. Finally, we introduce the class of fuzzy nondeterministic 2-tape automata (FNTA), show the equivalence between them and fuzzy linear automata.