The concepts stability and structural stability (robustness) are used often in systems biology. According to Kitano (2004) robustness is a fundamental property of evolvable complex biological systems. For that reason, the purpose of this review is to clarify: (a) how are strictly formulated concepts, such as stability and robustness of a dynamical system, used in computational systems biology; (b) what is meant by structural stability (robustness) in contemporary biology and how are stability and robustness distinguished from each other; and (c) why is it necessary to investigate whether a cell signal pathway is stable. We formulate the two concepts stability and structural stability (robustness) of a dynamical system with an arbitrary dimensionality, in the way they are known in mathematics and mechanics, and clarify the principal difference between them. We also consider how these two concepts are used in the analysis of a concrete biological system in systems biology. In the last section we formulate when, according to us, in biology (and in systems biology in particular), it should be said that a system (process) is stable, and when it is structurally stable.