The concept of fuzzy extremally disconnected spaces, due to B. Ghosh [ibid. 46, No. 2, 245-250 (1992; Zbl 0765.54004)] is generalized. A fuzzy bitopological space \((X,\tau_1,\tau_2)\) is said to be: (a) \((\tau_i, \tau_j)\)-fuzzy extremally disconnected \(((\tau_i, \tau_j)\)-FED) if the \(\tau_j\)-closure of every \(\tau_i\)-fo (fuzzy-open) set is \(\tau_i\)-fo in \(X\); (b) fuzzy pairwise extremally disconnected (FPED) if it is \((\tau_1, \tau_2)\)-FED and \((\tau_2, \tau_1)\)-FED. Some properties of FPED spaces are proved. A fuzzy bitopological space \((X,\tau_1, \tau_2)\) if FPED iff for each \(\tau_i\)-fo set \(A\) and each \(\tau_i\)-set \(B\), \(A\overline q B\), we have \(\tau_j\)-\(\text{cl} A\overline q\tau_j\)-\(\text{cl} B\). A fuzzy bitopological space \((X,\tau_1, \tau_2)\) is FPED iff every \((\tau_i, \tau_j)\)-\(\text{fso}\) set is a \((\tau_i, \tau_j)\)-\(\text{fpo}\) set. Some characterizations of FPED fuzzy bitopological spaces are proved, using the concepts of \(\tau_j\)-closure, \((\tau_j, \tau_i)\)-\(\theta\)-closure, \((\tau_0, \tau_i)\)-semi-closure, \(\tau_j\)-interior.