This study focuses on two extraclausal verbal constructions: free adjuncts (FAs: Not feeling at first the Pain of the Stroke, he wondered what was become of the Ball, DODDRIDGE-1747,10.72) and absolute constructions (ACs: Your Barrels being ready, strow the Bottom with Salt: DRUMMOND-1718,32.359). Adopting a quasi-synchronic approach applied to Modern and Present-Day English (PDE), we treat FAs and ACs as constructions (sufficiently frequent compositional form-meaning pairings); more specifically, we consider them two variants of a nested ‘nonfinite-periphery construction’ in which the parameter ±subject in the nonfinite periphery determines the ascription of the construction to either the FA or the AC type. In order to relate our findings to those of Río-Rey (2002) for Early Modern English and Kortmann (1991) for PDE, we analyse more than 3,000 FAs and ACs from the Penn Parsed Corpus of Modern British English, a multi-genre parsed corpus of Late Modern English (1700–1914), and from the British component of the International Corpus of English (ICE-GB). We hypothesise that FAs and ACs deserve unitary constructional treatment in Modern and PDE, on the basis of the statistical homogeneity of their frequencies, the fixation and reduction of the set of potential introducers, the comparable proportions of FAs and ACs semantically related to the clause, their preference for sentence-final position, and the increase of the less informative types.