Rational Classification of simple function space components for flag manifolds. Let $M(X,Y)$ denote the space of all continous functions between $X$ and $Y$ and $M_f(X,Y)$ the path component corresponding to a given map $f: X\rightarrow Y.$ When $X$ and $Y$ are classical flag manifolds, we prove the components of $M(X,Y)$ corresponding to simple'' maps $f$ are classified up to rational homotopy type by the dimension of the kernel of $f$ in degree two cohomology. In fact, these components are themselves all products of flag manifolds and odd spheres. Keywords:Rational homotopy theory, Sullivan-Haefliger model.Categories:55P62, 55P15, 58D99.