Nested Bethe ansatz for RTT--algebra of sp(4) type

We study the highest weight representations of the RTT--algebras for the R--matrix sp(4) type by the nested algebraic Bethe ansatz. These models were solved by Reshetikhin for sp(2n) but using a very special type of representation. The explicit construction of the Bethe vectors is carried out in the general case and the explicit formulae for the Bethe equations are derived. In conclusion, the direct generalization for sp(2n) is formulated.