  Let $X$ be a homogeneous space of a connected linear algebraic group $G$
defined over the field of complex numbers $\mathbb C$. Let $x\in X({\mathbb
C})$ be a point. We denote by $H$ the stabilizer of $x$ in $G$. When $H$ is
connected, we compute the topological fundamental group $\pi_1^{\rm
top}(X({\mathbb C}),x)$. Moreover, we compute the second homotopy group
$\pi_2^{\rm top}(X({\mathbb C}),x)$.
