  In this paper we construct an analogue of Iwahori-Hecke algebras of SL_2 over
2-dimensional local fields. After considering coset decompositions of double
cosets of a Iwahori subgroup, we define a convolution product on the space of
certain functions on SL_2, and prove that the product is well-defined. Then we
investigate the structure of the Hecke algebra. We determine the center of the
Hecke algebra and consider Iwahori-Matsumoto type relations.
