[en] The existence domains for one-dimensional acoustic solitons and double layers in complex (dusty) plasmas with two ion temperatures are obtained, using the fluid dynamic paradigm with a general polytropic equation of state. Dust-acoustic solitons are considered in a four-component plasma of negative dust grains, cool and very hot ions, and very hot electrons. Whereas in a dust-ion-electron plasma only negative potential solitons are supported, the presence of a second ion component allows positive potential solitons to occur as well. The existence domain in parameter space is delineated, in particular, also for the reduced three-component case in which there are no free electrons, all electrons being adsorbed onto the dust grains. Next, the ion-acoustic regime is considered. Both positive and negative potential dust-ion acoustic solitons and double layers are found, and their existence conditions in the parameter space of cool ion density and Mach number derived.