  We discuss upper and lower bounds for the size of gaps in the length spectrum
of negatively curved manifolds. For manifolds with algebraic generators for the
fundamental group, we establish the existence of exponential lower bounds for
the gaps. On the other hand, we show that the existence of arbitrary small gaps
is topologically generic: this is established both for surfaces of constant
negative curvature (Theorem 3.1), and for the space of negatively curved
metrics (Theorem 4.1). While arbitrary small gaps are topologically generic, it
is plausible that the gaps are not too small for almost every metric. One
result in this direction is presented in Section 5.
