  We investigate a family of peakon equations, labelled by two parameters $b$
and $\kappa$, all of which admit one-peakon solutions in a unified form. The
well known Camassa-Holm equation and Degasperis-Procesi equation are derived
from the b-family peakon equations by choosing $b=2$ and 3, respectively. For
all values of $b$, their two peakon-type solutions are shown in difference form
and in weak sense. At the same time, the dynamic behaviors are shown in
difference phenomenons, such as the peaked waves collide elastically in the
case $b=2$, while the peaked waves collide inelastically in other cases.
