We are concerned with Kolmogorov complexity of strings produced by non-deterministic algorithms. For this, we consider four classes of non-deterministic description modes : (i) Description modes in which the number of outputs computed by a program is finite, (ii) description modes in which the set of outputs is sparse, (iii) description modes for which each string has a unique minimal description, and lastly (iv) description modes for which the set of minimal length description is a prefix set.