  In this work, we consider the cosmological constraints on the interacting
dark energy models. We generalize the models considered previously by Guo {\it
et al.}, Costa and Alcaniz, and try to discuss two general types of models:
type I models are characterized by $\rho_{_X}/\rho_m=f(a)$ and $f(a)$ can be
any function of scale factor $a$, whereas type II models are characterized by
$\rho_m=\rho_{m0}\,a^{-3+\epsilon(a)}$ and $\epsilon(a)$ can be any function of
$a$. We obtain the cosmological constraints on the type I and II models with
power-law, CPL-like, logarithmic $f(a)$ and $\epsilon(a)$ by using the latest
observational data.
