Let $F: mathbb{C}^k;{ ightarrow};mathbb{C}^k$ be a dynamical system and let ${x_n}_{n{geq}0}$ denote an orbit of F. We study the relation between ${x_n}$ and pseudoorbits ${y_n}, y_0=x_0.;Here;y_{n+1}=F(y_n)+s_n.$ In general $y_n$ might diverge away from $x_n.$ Our main problem is whether there exists arbitrarily small $t_n$ so that if $ ilde{y}_{n+1}=F( ilde{y}_n)+s_n+t_n,$ then $ ilde{y}_n$ remains close to $x_n.$ This leads naturally to the concept of sustainable orbits, and their existence seems to be closely related to the concept of hyperbolicity, although they are not in general equivalent.