In this paper, the class of all bounded ultraweakly compact operators in Banach spaces is introduced and characterised in terms of their first and second conjugates. We analize the relationship between an ultraweakly compact operator and its conjugate. Examples of operators belonging to this class are exhibited. We also investigate the connection between ultraweak compactness of $T\in L\left(X,Y\right)$ and minimal subspaces of $Y^{\prime }$ and we present a result of factorisation for ultraweakly compact operators.