In this paper we shall consider thoroughly the Flnsler-Otsuki $F-O_2$ space whose theory for the $n$-dimension is based on [3] (\S1 and \S2). The intention of our work is the calculation of some basic formulae of the two-dimensional Finsler-Otsuki spaces. Using these formulae and the ideas of the determination of the coefficients of connection $'\Gamma^i_{jk}$ and $''\Gamma^i_{jk}$, from [3], we shall give the explicit formulae of $'\Gamma^i_{jk}$ and $''\Gamma^i_{jk}$ in $F-O_2$ spaces (Cf. (2.13) and (2.16)) and we shall prove that in the observed space, $''\Gamma^i_{jk}$ are of Cartain's type.