  We consider the so-called multi-mixed fractional Brownian motions (mmfBm) and
multi-mixed fractional Ornstein--Ulhenbeck processes (mmfOU). These processes
are constructed by mixing or by superimposing infinitely many independent
fractional Brownian motions and fractional Ornstein--Uhlenbeck processes,
respectively. We prove their existence as $L^2$ processes and study their path
properties, viz. H\"older continuity and conditional full support property. In
the finite mixture case we study their statistical parameter estimation by
using generalized method of moments (GMM) estimators.
