We construct wave and scattering operators for the Yang-Mills equations on Minkowski space,
M
0
≅
R
4
{{\mathbf {M}}_0} \cong {{\mathbf {R}}^4}
. Sufficiently regular solutions of the Yang-Mills equations on
M
0
{{\mathbf {M}}_0}
are known to extend uniquely to solutions of the corresponding equations on the universal cover of its conformal compactification,
M
~
≅
R
×
S
3
\tilde {\mathbf {M}} \cong {\mathbf {R}} \times {S^3}
. Moreover, the boundary of
M
0
{{\mathbf {M}}_0}
as embedded in
M
~
\tilde {\mathbf {M}}
is the union of "lightcones at future and past infinity",
C
±
{C_ \pm }
. We construct wave operators
W
±
{W_ \pm }
as continuous maps from a space
X
{\mathbf {X}}
of time-zero Cauchy data for the Yang-Mills equations to Hilbert spaces
H
(
C
±
)
{\mathbf {H}}({C_ \pm })
of Goursat data on
C
±
{C_ \pm }
. The scattering operator is then a homeomorphism
S
:
X
→
X
S:{\mathbf {X}} \to {\mathbf {X}}
such that
U
W
+
=
W
−
S
U{W_ + } = {W_ - }S
, where
U
:
H
(
C
+
)
→
H
(
C
−
)
U:{\mathbf {H}}({C_ + }) \to {\mathbf {H}}({C_ - })
is the linear isomorphism arising from a conformal transformation of
M
~
\tilde {\mathbf {M}}
mapping
C
−
{C_ - }
onto
C
+
{C_ + }
. The maps
W
±
{W_ \pm }
and
S
S
are shown to be smooth in a certain sense.