Abstract: Recall that a CW complex of dimension m is called spherical if it is m-1 connected. Let X be a Euclidean building. The Solomon-Tits theorem states that spherical buildings are spherical. Since small metric spheres in X are spherical buildings, it follows that small spheres in X are spherical. We generalize this result to spheres of arbitrary radius. For irreducible X, we argue that horospheres are also spherical.