We consider superconductors with a pp which is an odd function of ener
gy epsilon(k)BAR = epsilon(k)BAR - mu, i.e. vanishing everywhere on th
e Fermi surface; this is done within a BCS framework. Apart from the s
tandard phenomenology (density of states, penetration depth, NMR, C(v)
(T)), we also look at the stability of the superconducting state. It i
s stable to finite supercurrents (although with a normal fluid density
which increases with the supercurrent density), and a low concentrati
on of non-magnetic impurities affects the low-temperature transport pr
operties very weakly. We find two classes of odd-gap superconductors,
which strongly differ in their low-energy properties. For a certain pa
rameter range, most of the results resemble those for d-wave supercond
uctors (except for the effect of impurities).