This thesis presents a study of the speech of Welsh-English bilinguals to determine the extent and manner of the structural influence of English on Welsh, specifically the phenomenon of convergence, which is described as the increase in frequency of use of a construction (e. g. word order) In one language due to the prevalence of that construction in another language with which its speakers are in contact. I take two approaches to measure convergence, using Welsh-English conversational data which were specially-collected for a 40 hour corpus. First, I adapt the Matrix Language Frame model (Myers-Scotton 2002), usable to Identify the language from which clause morphosyntax is sourced, to identify convergence. I propose the concept of a dichotomous Matrix Language, which is where there is conflicting evidence for which language provides clause structure. In testing the model on speech from six speakers, I find that, with few exceptions, Welsh is the source of the structure In the majority of clauses analysed. I Interpret this to show that word-order convergence In these data Is limited Insofar as using the Matrix Language Frame model indicates. Second, I analyse the speech of 28 bilinguals for evidence of the deletion of the initial auxiliary verb in periphrastic constructions Involving an auxiliary form of bod `be' and a 2"d person singular pronominal subject ti. Auxiliary deletion (AD) in such clauses results In a clause-initial subject, which I compare to English SVO word-order. I find that AD In such contexts Is very common In these data, and is also found In clauses with a different subject. Analysis of age variation In the data Indicates that AD In Welsh has become more common In recent years. I propose that an Increase to subject-initial clauses In Welsh may be a change in progress, which I Interpret to be in part due to convergence to English.