The expansion part of the trial will be used to further assess the tolerability of AZD2014 in combination with weekly paclitaxel. For the 3 days on 4 days off schedule 10 patients with ovarian cancer and 15 patients with squamous lung cancer will be enrolled and treated at the MTD established from the dose escalation phase. Accrual to these expansion arms may commence as soon as the MTD is determined and proceed in parallel with the dose escalation phase of the 2 days on 5 days off schedule. Once the MTD has been determined for the 2 days on 5 days off schedule 15 patients with squamous lung cancer may be enrolled.