Around 1980 two generalizations of the theory of linearly ordered fields appeared in the literature: Becker's theory of orderings of higher level on fields (J. Reine Angew. Math. 307/308 (1979)8) and Holland's theory of ∗-orderings on skew-fields with involution (J. Algebra 101 (1) (1986) 16–46). The aim of this paper is to unify both theories. In Section 1 we define (higher level) ∗-signatures on domains with involution which correspond to higher level preorderings in Becker's theory. The subclasses of 2-cyclic and cyclic ∗-signatures correspond to complete preorderings and orderings respectively. We prove a necessary and sufficient condition for extendability of ∗-signatures from Ore domains to skew-fields of fractions. In Section 2 we define the set of bounded elements of a ∗-signature on a skew field with involution. If the skew field contains a central element i such that i 2=−1 and i ∗=−i and the ∗-signature is 2-cyclic then the set of bounded elements is an invariant valuation ring. An example shows that the assumption on i cannot be omitted. In Section 3 we define extended ∗-signatures and prove that every 2-cyclic ∗-signature on a skew field D with i∈ Z( D) is a restriction of some extended ∗-signature. In Section 4 we define extended ∗-preorderings as positive cones of extended ∗-signatures. We show that every ∗-preordering which is a restriction of an extended ∗-preordering is equal to the intersection of all ∗-orderings containing it. The assumption i∈ Z( D) is not required. Section 5 presents auxilliary material for the proof of the weak isotropy principle for higher level ∗-signatures which is given in Section 6.