  Yangian-like algebras, associated with current R-matrices, different from the
Yang ones, are introduced. These algebras are of two types. The so-called
braided Yangians are close to the Reflection Equation algebras, arising from
involutive or Hecke symmetries. The Yangians of RTT type are close to the
corresponding RTT algebras. Some properties of these two classes of the
Yangians are studied. Thus, evaluation morphisms for them are constructed,
their bi-algebra structures are described, and quantum analogs of certain
symmetric polynomials, in particular, quantum determinants, are introduced. It
is shown that in any braided Yangian this determinant is always central,
whereas in the Yangians of RTT type it is not in general so. Analogs of the
Cayley-Hamilton-Newton identity in the braided Yangians are exhibited. A
bozonization of the braided Yangians is performed.
