Propositional algorithmic logic PAL is a propositional counterpart of algorithmic logics. It investigates properties of program connectives: begin...end, while...do, if..then..else, or .... PAL supplies tools for reasoning about programs constructed from program variables by means of program connectives and about their algorithmic properties. Sound rules of inference and tautologies of PAL are as important in analysis of programs (e.g. verification) as tautologies of classical propositional calculus. On the other hand propositional algorithmic theories are of highest interest, since they can capture properties of data structures and also algorithmic properties of behaviours of concurrent systems. We proved that the semantical and the syntactical consequence operations coincide (completeness property) and that the model existence theorem holds.