Disclosed herein are for example, liquid aqueous compositions that include for example an ester or salt of levodopa, or an ester or salt of carbidopa, and methods for treating neurological or movement diseases or disorders such as restless leg syndrome, Parkinsons disease, secondary parkinsonism, Huntingtons disease, Parkinsons like syndrome, PSP, MSA, ALS, Shy-Drager syndrome, dystonia, and conditions resulting from brain injury including carbon monoxide or manganese intoxication, using substantially continuous administration of levodopa and/or carbidopa or ester and/or salt thereof.