  We present an exact method to study four-quark systems based on the
hyperspherical harmonics formalism. We apply it to several physical systems of
interest containing two heavy and two light quarks using different quark-quark
potentials. Our conclusions mark the boundaries for the possible existence of
compact, non-molecular, four-quark bound states. While $QQ\bar n \bar n$ states
may be stable in nature, the stability of $Q\bar Qn \bar n$ states would imply
the existence of quark correlations not taken into account by simple quark
dynamical models
