Detecting negation and speculation in language has been a task of considerable interest to the biomedical community, as it is a key component of Information Extraction systems from Biomedical documents. Prior work has individually addressed Negation Detection and Speculation Detection, and both have been addressed in the same way, using 2 stage pipelined approach: Cue Detection followed by Scope Resolution. In this paper, we propose Multitask learning approaches over 2 sets of tasks: Negation Cue Detection & Speculation Cue Detection, and Negation Scope Resolution & Speculation Scope Resolution. We utilise transformer-based architectures like BERT, XLNet and RoBERTa as our core model architecture, and finetune these using the Multitask learning approaches. We show that this Multitask Learning approach outperforms the single task learning approach, and report new state-of-the-art results on Negation and Speculation Scope Resolution on the BioScope Corpus and the SFU Review Corpus.