According to the provisions of section 313 of the Companies Act, 1956, an Alternate Director is a person appointed by the Board if so authorised by the Articles or by a resolution passed by the company in the general meeting to act for a director called "the original director" during his absence for a period of not less than three months from the State in which meetings of the Board are ordinarily held. Generally, the alternate directors are appointed for a person who is Non-resident Indian or for foreign collaborators of a company. Therefore you can see an Alternate Director can not be appointed in the event of Death of a Director.
So you can appointment pursuant to sec 262 to fill the Casual vacancy.
Subject to the provisions of the articles, the Board of directors can fill up any casual vacancy arising prematurely in the office of any director appointed by the company in general meeting. If an office of a director is vacated by the person concerned before expiry of his term, the resulting casual vacancy can be filled by the Board only at a meeting. The person appointed will act as director up to the date at which the "original" director would have ceased to be director. This provision does not apply to a private company. The provision, if any, in the Articles will apply. E-Form 32 for appointment of casual director should be filed by the company electronically to the Registrar within 30 days from the date of appointment.
Where the Director in whose place new person is appointed is a Rotational Director and he was to vacate his office at coming AGM, Then the person so appointed U/S 262 shall not be considered as Director for appointment U/S 256 only because he has been appointed in place of Rotaional Director.
If he wants to stand for Directorship, He will have to follow Section 257.
IT SHOULD BE NOTED THAT SECTION 262 IS APPLICABLE ONLY ON PUBLIC LTD AND PVT LTD WHICH IS SUBSIDIARY OF PUBLIC LTD AND ALSO SUBJECT TO THE PROVISION OF AOA.