BD-FRW universe filled with imperfect fluid having bulk viscosity is investigated under the framework of Israel-Stewart-Hiscock causal theory. The field equations have been solved by using the relation φ=KRα where K and α are constants, between the Brans-Dicke scalar field φ{symbol} and the scale factor R. This relation, in fact, leads to a constant deceleration parameter q. It is shown that the constancy of the deceleration parameter permits only two possibilities i.e. either H=constant with m=1 or m=(1+b -α)/(2(1+b) -α), irrespective of the value of e{open}. © 1995 Indian Academy of Sciences.