Starting from the definition of generalized Riemannian space $(GR_N)$ [1], in which a non-symmetric basic tensor $g_{ij}$ is introduced, in the present paper a generalized K\"ahlerian space $G\underset{2}{K}{}_N$ of the second kind is defined, as a $GR_N$ with almost complex structure $F^h_i$ , that is covariantly constant with respect to the second kind of covariant derivative (equation (2.3)). Several theorems are proved. These theorems are generalizations of the corresponding theorems relating to $K_N$. The relations between $F^h_i$ and four curvature tensors from $GR_N$ are obtained.