  We present new spherically symmetric, dyonic soliton and black hole solutions
of the ${\mathfrak {su}}(N)$ Einstein-Yang-Mills equations in four-dimensional
asymptotically anti-de Sitter space-time. The gauge field has nontrivial
electric and magnetic components and is described by $N-1$ magnetic gauge field
functions and $N-1$ electric gauge field functions. We explore the phase space
of solutions in detail for ${\mathfrak {su}}(2)$ and ${\mathfrak {su}}(3)$
gauge groups. Combinations of the electric gauge field functions are monotonic
and have no zeros; in general the magnetic gauge field functions may have
zeros. The phase space of solutions is extremely rich, and we find solutions in
which the magnetic gauge field functions have more than fifty zeros. Of
particular interest are solutions for which the magnetic gauge field functions
have no zeros, which exist when the negative cosmological constant has
sufficiently large magnitude. We conjecture that at least some of these
nodeless solutions may be stable under linear, spherically symmetric,
perturbations.
