This is a multi-centre, randomised, placebo-controlled, double blind, parallel group 3-arm study (including montelukast as an active comparator) designed to compare the efficacy and safety of a once daily dose of ADC3680 with placebo in subjects with inadequately-controlled asthma despite receiving a low to moderate dose of an ICS controller therapy, over a 10 week treatment period. At the end of the 10 week treatment period open label montelukast (10 mg) will be added to ADC3680 and placebo arms for a two week extension period to assess whether efficacy of ADC3680 is enhanced by the addition of montelukast compared with montelukast alone. The montelukast arm will continue with 10 mg montelukast alone.