Both are deterministic CFL
L2... Insert symbol into stack until C doesn't appear... If C the skip it and compare top of stack with input symbol.. Because of C it becomes deterministic...
L1..
If "a " comes then we can't decide ...but after "a" , "a" or "b" comes then first part of given language is considered and if epsilon comes then second part need to consider... We can easily recognize it with the help of DPDA...