  We study non-topological solitons, so called Q-balls, which carry a
non-vanishing Noether charge and arise as lump solutions of self-interacting
complex scalar field models. Explicit examples of new axially symmetric
non-spinning Q-ball solutions that have not been studied so far are constructed
numerically. These solutions can be interpreted as angular excitations of the
fundamental $Q$-balls and are related to the spherical harmonics.
Correspondingly, they have higher energy and their energy densities possess two
local maxima on the positive z-axis.
  We also study two Q-balls interacting via a potential term in (3+1)
dimensions and construct examples of stationary, solitonic-like objects in
(3+1)-dimensional flat space-time that consist of two interacting global scalar
fields. We concentrate on configurations composed of one spinning and one
non-spinning Q-ball and study the parameter-dependence of the energy and
charges of the configuration.
  In addition, we present numerical evidence that for fixed values of the
coupling constants two different types of 2-Q-ball solutions exist: solutions
with defined parity, but also solutions which are asymmetric with respect to
reflexion through the x-y-plane.
