  The interplay between intrinsic and surface/interface-induced magnetic
anisotropies strongly in- fluences magnetization processes in nanomagnetic
systems. We develop a micromagnetic theory to describe the field-driven
reorientation in nanomagnets with cubic and uniaxial anisotropies. Spin
configurations in competing phases and parameters of accompanying multidomain
states are calculated as functions of the applied field and the magnetic
anisotropies. The constructed magnetic phase diagrams allow to classify
different types of the magnetization reversal and to provide detailed analysis
of the switching processes in magnetic nanostructures. The calculated
magnetization profiles of isolated domain walls show that the equilibrium
parameters of such walls are extremely sensitive to applied magnetic field and
values of the competing anisotropies and can vary in a broad range. For
nanolayers with perpendicular anisotropy the geometrical parameters of stripe
domains have been calculated as functions of a bias field. The results are
applied to analyse the magnetization processes as observed in various
nanosystems with competing anisotropies, mainly, in diluted magnetic
semiconductor films (Ga,Mn)As.
