On completion of the dose escalation phase of the study patients with ovarian cancer and squamous cell lung cancer will be treated at the MTD established for each dosing schedule. A minimum of 10 ovarian cancer patients and 15 squamous cell lung patients will be enrolled to the 3 days on, 4 days off schedule. Whilst a minimum of 10 squamous cell cancer patients will be enrolled to the 2 days on, 5 days off schedule to further assess the tolerability of the combination of AZD2014 and paclitaxel.