The construction projects are hardly completed on schedule and budget, and poor claims and dispute management are among the factors responsible for this performance issue. Critical claims in construction remain unresolved by negotiation and understanding between the parties but end up in advanced dispute resolution techniques. Quantity Surveyors are experts in contract administrations and are involved in all the stages of the construction projects, have not been given adequate attention in construction claim management studies. This study assesses the perception of Quantity Surveyors on the Critical claims and their impact on construction project delivery in Nigeria. The snow sampling technique was used to administer the structured questionnaire. With a Cronbach's alpha coefficient of over 0.80, the gathered data were analysed using mean score analysis and the Mann-Whitney H test. It was found that the critical claims in construction are payment-related claims (mean=4.92; SD=0.2780), contractual claims (mean=4.55; SD=0.8837), change claims (mean=4.54; SD=0.8423), extra work claims (mean=4.43; SD=0.9974), delay claims (mean=4.36; SD=1.1683), and different site condition claims (mean=4.36; SD=1.0826). Also, the major impacts of claims in construction project delivery are delays in project completion cost overrun, poor quality of work, the adversarial relationship among parties, loss of profits, and loss of job opportunities. Effective contract administration and management are central to claim management and events capable of causing drawbacks to the progress of the work should be avoided by the contracted parties.