Two nonperturbative methods by means of the transfer-matrix finite-size-sca
ling and Monte Carlo simulations are used to investigate the spin-1 Ashkin-
Teller model (ATM). We have obtained rich phase diagrams with first- and se
cond-order phase transitions with several multicritical points of higher or
der. Also this model exhibits a partially ordered phase PO2 which does not
exist in the spin-1/2 Ashkin-Teller model (ATM). Finally, the critical beha
vior of this model is discussed. [S0163-1829(99)00609-8).