In this paper we study del Pezzo fibrations z: X→ℙ1 of degree 1 and 2 such that X is smooth, rk Pic( X)=2 and These are examples of smooth birationally rigid 3-fold Mori fibre spaces. We describe all birational transformations of the 3-fold X into elliptic fibrations, fibrations of surfaces of Kodaira dimension zero, and canonical Fano 3-folds.