The present invention provides an agricultural or horticultural fungicide including an effective amount of an amino-acid derivative represented by the formula: ##STR1## wherein R.sup.1 represents a lower alkyl group (optionally having at least one same or different substituent of a halogen atom, an alkoxy group, and a cyano group), R.sup.2 represents an ethyl group, or an n-propyl group, R.sup.3 represents a hydrogen atom or a lower alkyl group, R.sup.4 represents a hydrogen atom, R.sup.5, R.sup.6, and R.sup.7 independently represent a hydrogen atom or a lower alkyl group, R.sup.8 represents a hydrogen atom, or a lower alkyl group, Z.sup.1 and Z.sup.2 independently represent an oxygen atom or a sulfur atom, Z.sup.3 represents an oxygen atom, or a sulfur atom, Q represents a phenyl group, m represents an integer from 0 to 2, and n represents 0 or 1.The amino-acid amide derivatives according to the present invention exhibit superior control of cucumber downy mildew (Pseudoperonospora cubensis), tomato late blight (Phytophthora infestans), and grape downy mildew (Plasmopara viticola), and are effective for potato late blight (Phytophthora infestans). In addition, the agricultural or horticultural fungicides of the present invention are also characterized in that they are not harmful chemicals and exhibit excellent characteristics such as systemic action, residual activity, and persistence after rain-fall.